具有参数反射的两点边值问题
IF 1.9
3区 数学
Q1 MATHEMATICS
Nai-Sher Yeh
{"title":"具有参数反射的两点边值问题","authors":"Nai-Sher Yeh","doi":"10.1155/2023/6010530","DOIUrl":null,"url":null,"abstract":"We consider the following two-point boundary value problems <span><svg height=\"14.8655pt\" style=\"vertical-align:-3.4294pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.4361 40.64 14.8655\" width=\"40.64pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,6.994,-5.741)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,10.033,-5.741)\"><use xlink:href=\"#g50-31\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.84,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,18.338,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,25.606,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,33.009,0)\"></path></g></svg><span></span><svg height=\"14.8655pt\" style=\"vertical-align:-3.4294pt\" version=\"1.1\" viewbox=\"43.4961838 -11.4361 54.92 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xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,10.738,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"15.8311838 -9.28833 15.146 11.5564\" width=\"15.146pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,15.881,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,23.565,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,28.063,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"33.1561838 -9.28833 33.494 11.5564\" width=\"33.494pt\" xmlns=\"http://www.w3.org/2000/svg\" 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style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"91.4161838 -9.28833 27.107 11.5564\" width=\"27.107pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,91.466,0)\"><use xlink:href=\"#g113-118\"></use></g><g transform=\"matrix(.013,0,0,-0.013,98.46,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,102.958,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,110.643,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,115.141,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span></span> and <span><svg height=\"14.8655pt\" style=\"vertical-align:-3.4294pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.4361 40.64 14.8655\" width=\"40.64pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-118\"></use></g><g 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xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,189.454,0)\"><use xlink:href=\"#g117-33\"></use></g><g transform=\"matrix(.013,0,0,-0.013,197.085,0)\"><use xlink:href=\"#g113-105\"></use></g><g transform=\"matrix(.013,0,0,-0.013,203.794,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,208.292,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,215.559,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> in <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 13.702 11.5564\" width=\"13.702pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.738,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"15.8311838 -9.28833 15.146 11.5564\" width=\"15.146pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,15.881,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,23.565,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,28.063,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"33.1561838 -9.28833 33.494 11.5564\" width=\"33.494pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,33.206,0)\"><use xlink:href=\"#g113-118\"></use></g><g transform=\"matrix(.013,0,0,-0.013,40.201,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,44.699,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,50.939,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,59.069,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"70.28118380000001 -9.28833 17.503 11.5564\" width=\"17.503pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,70.331,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,80.203,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"91.4161838 -9.28833 27.107 11.5564\" width=\"27.107pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,91.466,0)\"><use xlink:href=\"#g113-118\"></use></g><g transform=\"matrix(.013,0,0,-0.013,98.46,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,102.958,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,110.643,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,115.141,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span></span> by setting <span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 17.204 13.8595\" width=\"17.204pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-105\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.34,0)\"></path></g></svg><span></span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"20.7861838 -11.5914 25.833 13.8595\" width=\"25.833pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,20.836,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,28.021,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.967,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,37.465,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,43.705,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"48.7981838 -11.5914 12.46 13.8595\" width=\"12.46pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,48.848,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,56.533,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> and <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 13.994 12.7178\" width=\"13.994pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-104\"></use></g><g transform=\"matrix(.013,0,0,-0.013,11.03,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"17.576183800000003 -9.28833 13.702 12.7178\" width=\"13.702pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,17.626,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,22.124,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,28.364,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"33.457183799999996 -9.28833 22.719 12.7178\" width=\"22.719pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,33.507,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,41.191,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,48.595,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"59.0811838 -9.28833 29.961 12.7178\" width=\"29.961pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,59.131,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,70.914,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,76.69,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"92.7511838 -9.28833 8.474 12.7178\" width=\"8.474pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,92.801,0)\"><use xlink:href=\"#g113-83\"></use></g></svg></span> being a Caratheodory function. When <span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 9.544 13.8595\" width=\"9.544pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.58,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"11.6731838 -11.5914 16.597 13.8595\" width=\"16.597pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,11.723,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,21.456,0)\"><use xlink:href=\"#g117-173\"></use></g></svg><span></span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"31.902183800000003 -11.5914 25.834 13.8595\" width=\"25.834pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,31.952,0)\"><use xlink:href=\"#g113-77\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,39.137,-5.741)\"><use xlink:href=\"#g50-50\"></use></g><g transform=\"matrix(.013,0,0,-0.013,44.084,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,48.582,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,54.822,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"59.9151838 -11.5914 12.486 13.8595\" width=\"12.486pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,59.965,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,67.649,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>,</span></span> <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 34.106 11.5564\" width=\"34.106pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-98\"></use></g><g transform=\"matrix(.013,0,0,-0.013,6.58,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,11.078,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,18.345,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.475,0)\"></path></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"37.6881838 -9.28833 6.475 11.5564\" width=\"6.475pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,37.738,0)\"></path></g></svg></span> for <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 17.763 11.5564\" width=\"17.763pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.899,0)\"><use xlink:href=\"#g117-173\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"21.3451838 -9.28833 13.702 11.5564\" width=\"13.702pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,21.395,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,25.893,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.133,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"37.2261838 -9.28833 12.43 11.5564\" width=\"12.43pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,37.276,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,44.96,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> a.e. with strict inequality on a positive measurable subset of <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 13.702 11.5564\" width=\"13.702pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.738,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"15.8311838 -9.28833 12.378 11.5564\" width=\"12.378pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,15.881,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,23.565,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>,</span></span> and <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 25.546 12.7178\" width=\"25.546pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,3.419,0)\"><use xlink:href=\"#g113-104\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.817,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,15.315,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,22.582,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"27.6761838 -9.28833 26.174 12.7178\" width=\"26.174pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,27.726,0)\"><use xlink:href=\"#g113-118\"></use></g><g transform=\"matrix(.013,0,0,-0.013,34.72,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,39.218,0)\"><use xlink:href=\"#g113-9\"></use></g><g transform=\"matrix(.013,0,0,-0.013,46.269,0)\"><use xlink:href=\"#g117-93\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"57.482183799999994 -9.28833 47.212 12.7178\" width=\"47.212pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,57.532,0)\"><use xlink:href=\"#g113-98\"></use></g><g transform=\"matrix(.013,0,0,-0.013,64.112,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,68.61,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,75.877,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,80.375,0)\"><use xlink:href=\"#g113-9\"></use></g><g transform=\"matrix(.013,0,0,-0.013,83.794,0)\"><use xlink:href=\"#g113-118\"></use></g><g transform=\"matrix(.013,0,0,-0.013,90.788,0)\"><use xlink:href=\"#g113-9\"></use></g><g transform=\"matrix(.013,0,0,-0.013,97.113,0)\"><use xlink:href=\"#g117-36\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"107.5991838 -9.28833 22.886 12.7178\" width=\"22.886pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,107.649,0)\"><use xlink:href=\"#g113-99\"></use></g><g transform=\"matrix(.013,0,0,-0.013,113.75,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,118.248,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,125.516,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> for <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 17.763 11.5564\" width=\"17.763pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-121\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.899,0)\"><use xlink:href=\"#g117-173\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"21.3451838 -9.28833 13.702 11.5564\" width=\"13.702pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,21.395,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,25.893,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.133,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"37.2261838 -9.28833 12.43 11.5564\" width=\"12.43pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,37.276,0)\"><use xlink:href=\"#g113-238\"></use></g><g transform=\"matrix(.013,0,0,-0.013,44.96,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> a.e. as well as sufficiently large <span><svg height=\"11.439pt\" style=\"vertical-align:-2.15067pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 13.9835 11.439\" width=\"13.9835pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-9\"></use></g><g transform=\"matrix(.013,0,0,-0.013,3.419,0)\"><use xlink:href=\"#g113-118\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.413,0)\"><use xlink:href=\"#g113-9\"></use></g></svg>,</span> several existence theorems will be obtained, with or without a sign condition.","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":"58 4","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Two-Point Boundary Value Problem with Reflection of the Argument\",\"authors\":\"Nai-Sher Yeh\",\"doi\":\"10.1155/2023/6010530\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the following two-point boundary value problems <span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -11.4361 40.64 14.8655\\\" width=\\\"40.64pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,6.994,-5.741)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,10.033,-5.741)\\\"><use xlink:href=\\\"#g50-31\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.84,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,18.338,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,25.606,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,33.009,0)\\\"></path></g></svg><span></span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"43.4961838 -11.4361 54.92 14.8655\\\" width=\\\"54.92pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,43.546,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,50.54,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,55.038,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,65.628,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,76.164,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,83.432,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,90.835,0)\\\"><use xlink:href=\\\"#g117-36\\\"></use></g></svg><span></span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"101.3211838 -11.4361 22.128 14.8655\\\" width=\\\"22.128pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,101.371,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,108.77,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,113.268,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,120.535,0)\\\"></path></g></svg><span></span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"125.6281838 -11.4361 60.145 14.8655\\\" width=\\\"60.145pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,125.678,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,132.672,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,137.17,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,147.76,0)\\\"><use xlink:href=\\\"#g117-33\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,158.296,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,165.564,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,170.062,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,178.192,0)\\\"></path></g></svg><span></span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"189.4041838 -11.4361 23.714 14.8655\\\" width=\\\"23.714pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,189.454,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,196.163,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,200.661,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,207.928,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> in <span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 13.702 11.5564\\\" width=\\\"13.702pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,4.498,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,10.738,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"15.8311838 -9.28833 15.146 11.5564\\\" width=\\\"15.146pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,15.881,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,23.565,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,28.063,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"33.1561838 -9.28833 33.494 11.5564\\\" width=\\\"33.494pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,33.206,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,40.201,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,44.699,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,50.939,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,59.069,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"70.28118380000001 -9.28833 17.503 11.5564\\\" width=\\\"17.503pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,70.331,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,80.203,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"91.4161838 -9.28833 27.107 11.5564\\\" width=\\\"27.107pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,91.466,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,98.46,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,102.958,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,110.643,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,115.141,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span></span> and <span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -11.4361 40.64 14.8655\\\" width=\\\"40.64pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,6.994,-5.741)\\\"><use xlink:href=\\\"#g50-31\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,10.033,-5.741)\\\"><use xlink:href=\\\"#g50-31\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.84,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,18.338,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,25.606,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,33.009,0)\\\"><use xlink:href=\\\"#g117-36\\\"></use></g></svg><span></span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"43.4961838 -11.4361 79.953 14.8655\\\" width=\\\"79.953pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,43.546,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,50.54,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,55.038,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,65.628,0)\\\"><use xlink:href=\\\"#g117-33\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,76.164,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,83.432,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,90.835,0)\\\"><use xlink:href=\\\"#g117-33\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,101.371,0)\\\"><use xlink:href=\\\"#g113-104\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,108.77,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,113.268,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,120.535,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"125.6281838 -11.4361 60.145 14.8655\\\" width=\\\"60.145pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,125.678,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,132.672,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,137.17,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,147.76,0)\\\"><use xlink:href=\\\"#g117-33\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,158.296,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,165.564,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,170.062,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,178.192,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"14.8655pt\\\" style=\\\"vertical-align:-3.4294pt\\\" version=\\\"1.1\\\" viewbox=\\\"189.4041838 -11.4361 31.373 14.8655\\\" width=\\\"31.373pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,189.454,0)\\\"><use xlink:href=\\\"#g117-33\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,197.085,0)\\\"><use xlink:href=\\\"#g113-105\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,203.794,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,208.292,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,215.559,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> in <span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 13.702 11.5564\\\" width=\\\"13.702pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,4.498,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,10.738,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"15.8311838 -9.28833 15.146 11.5564\\\" width=\\\"15.146pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,15.881,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,23.565,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,28.063,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"33.1561838 -9.28833 33.494 11.5564\\\" width=\\\"33.494pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,33.206,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,40.201,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,44.699,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,50.939,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,59.069,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"70.28118380000001 -9.28833 17.503 11.5564\\\" width=\\\"17.503pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,70.331,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,80.203,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"91.4161838 -9.28833 27.107 11.5564\\\" width=\\\"27.107pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,91.466,0)\\\"><use xlink:href=\\\"#g113-118\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,98.46,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,102.958,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,110.643,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,115.141,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span></span> by setting <span><svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -11.5914 17.204 13.8595\\\" width=\\\"17.204pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-105\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,10.34,0)\\\"></path></g></svg><span></span><svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"20.7861838 -11.5914 25.833 13.8595\\\" width=\\\"25.833pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,20.836,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,28.021,-5.741)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,32.967,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,37.465,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,43.705,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"48.7981838 -11.5914 12.46 13.8595\\\" width=\\\"12.46pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,48.848,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,56.533,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> and <span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 13.994 12.7178\\\" width=\\\"13.994pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-104\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,11.03,0)\\\"></path></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"17.576183800000003 -9.28833 13.702 12.7178\\\" width=\\\"13.702pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,17.626,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,22.124,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,28.364,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"33.457183799999996 -9.28833 22.719 12.7178\\\" width=\\\"22.719pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,33.507,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,41.191,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,48.595,0)\\\"></path></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"59.0811838 -9.28833 29.961 12.7178\\\" width=\\\"29.961pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,59.131,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,70.914,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,76.69,0)\\\"></path></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"92.7511838 -9.28833 8.474 12.7178\\\" width=\\\"8.474pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,92.801,0)\\\"><use xlink:href=\\\"#g113-83\\\"></use></g></svg></span> being a Caratheodory function. When <span><svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -11.5914 9.544 13.8595\\\" width=\\\"9.544pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,6.58,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"11.6731838 -11.5914 16.597 13.8595\\\" width=\\\"16.597pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,11.723,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,21.456,0)\\\"><use xlink:href=\\\"#g117-173\\\"></use></g></svg><span></span><svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"31.902183800000003 -11.5914 25.834 13.8595\\\" width=\\\"25.834pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,31.952,0)\\\"><use xlink:href=\\\"#g113-77\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,39.137,-5.741)\\\"><use xlink:href=\\\"#g50-50\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,44.084,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,48.582,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,54.822,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><span><svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"59.9151838 -11.5914 12.486 13.8595\\\" width=\\\"12.486pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,59.965,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,67.649,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg>,</span></span> <span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 34.106 11.5564\\\" width=\\\"34.106pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-98\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,6.58,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,11.078,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,18.345,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,26.475,0)\\\"></path></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"37.6881838 -9.28833 6.475 11.5564\\\" width=\\\"6.475pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,37.738,0)\\\"></path></g></svg></span> for <span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 17.763 11.5564\\\" width=\\\"17.763pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-121\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,10.899,0)\\\"><use xlink:href=\\\"#g117-173\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"21.3451838 -9.28833 13.702 11.5564\\\" width=\\\"13.702pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,21.395,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,25.893,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,32.133,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"37.2261838 -9.28833 12.43 11.5564\\\" width=\\\"12.43pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,37.276,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,44.96,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> a.e. with strict inequality on a positive measurable subset of <span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 13.702 11.5564\\\" width=\\\"13.702pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,4.498,0)\\\"><use xlink:href=\\\"#g113-49\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,10.738,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><span><svg height=\\\"11.5564pt\\\" style=\\\"vertical-align:-2.26807pt\\\" version=\\\"1.1\\\" viewbox=\\\"15.8311838 -9.28833 12.378 11.5564\\\" width=\\\"12.378pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,15.881,0)\\\"><use xlink:href=\\\"#g113-238\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,23.565,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg>,</span></span> and <span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 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引用次数: 0
摘要
我们通过设置和作为卡拉多函数来考虑下列两点边值问题。当在正可测子集上具有严格不等式的a.e.，且a.e.足够大时，将得到若干存在性定理，不论有无符号条件。本文章由计算机程序翻译，如有差异，请以英文原文为准。
A Two-Point Boundary Value Problem with Reflection of the Argument
We consider the following two-point boundary value problems in and in by setting and being a Caratheodory function. When , for a.e. with strict inequality on a positive measurable subset of , and for a.e. as well as sufficiently large , several existence theorems will be obtained, with or without a sign condition.
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来源期刊
Journal of Function Spaces
MATHEMATICS, APPLIEDMATHEMATICS -MATHEMATICS
CiteScore
4.10
自引率
10.50%
发文量
451
审稿时长
15 weeks
期刊介绍：
Journal of Function Spaces (formerly titled Journal of Function Spaces and Applications) publishes papers on all aspects of function spaces, functional analysis, and their employment across other mathematical disciplines. As well as original research, Journal of Function Spaces also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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