{"title":"具有非局部边界条件的非线性Sturm-Liouville问题的存在性理论","authors":"D. Maroncelli, Jesús F. Rodríguez","doi":"10.7153/DEA-2018-10-09","DOIUrl":null,"url":null,"abstract":"In this work we provide conditions for the existence of solutions to nonlinear SturmLiouville problems of the form (p(t)x′(t))′ +q(t)x(t)+λx(t) = f (x(t)) subject to non-local boundary conditions ax(0)+bx′(0) = η1(x) and cx(1)+dx′(1) = η2(x). Our approach will be topological, utilizing Schaefer’s fixed point theorem and the LyapunovSchmidt procedure.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"11 1","pages":"147-161"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Existence theory for nonlinear Sturm-Liouville problems with non-local boundary conditions\",\"authors\":\"D. Maroncelli, Jesús F. Rodríguez\",\"doi\":\"10.7153/DEA-2018-10-09\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work we provide conditions for the existence of solutions to nonlinear SturmLiouville problems of the form (p(t)x′(t))′ +q(t)x(t)+λx(t) = f (x(t)) subject to non-local boundary conditions ax(0)+bx′(0) = η1(x) and cx(1)+dx′(1) = η2(x). Our approach will be topological, utilizing Schaefer’s fixed point theorem and the LyapunovSchmidt procedure.\",\"PeriodicalId\":11162,\"journal\":{\"name\":\"Differential Equations and Applications\",\"volume\":\"11 1\",\"pages\":\"147-161\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/DEA-2018-10-09\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/DEA-2018-10-09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Existence theory for nonlinear Sturm-Liouville problems with non-local boundary conditions
In this work we provide conditions for the existence of solutions to nonlinear SturmLiouville problems of the form (p(t)x′(t))′ +q(t)x(t)+λx(t) = f (x(t)) subject to non-local boundary conditions ax(0)+bx′(0) = η1(x) and cx(1)+dx′(1) = η2(x). Our approach will be topological, utilizing Schaefer’s fixed point theorem and the LyapunovSchmidt procedure.
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