A. Martinez, E. V. Castelani, C. Martinez, G. Bressan, Roberto Molina de Souza
{"title":"用非线性规划方法辅助求解三阶三点非齐次边值问题","authors":"A. Martinez, E. V. Castelani, C. Martinez, G. Bressan, Roberto Molina de Souza","doi":"10.7153/DEA-2021-13-03","DOIUrl":null,"url":null,"abstract":". In this work, we consider a third order equation of three points with non-homogeneous conditions at the border. We apply Avery Peterson’s theorem, and present a theoretical result that guarantees the existence of multiple solutions to this problem under certain conditions. In addition, we present non-trivial examples and a new numerical method based on optimization is introduced.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multiple solutions to a third-order three-point nonhomogeneous boundary value problem aided by nonlinear programming methods\",\"authors\":\"A. Martinez, E. V. Castelani, C. Martinez, G. Bressan, Roberto Molina de Souza\",\"doi\":\"10.7153/DEA-2021-13-03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this work, we consider a third order equation of three points with non-homogeneous conditions at the border. We apply Avery Peterson’s theorem, and present a theoretical result that guarantees the existence of multiple solutions to this problem under certain conditions. In addition, we present non-trivial examples and a new numerical method based on optimization is introduced.\",\"PeriodicalId\":51863,\"journal\":{\"name\":\"Differential Equations & Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations & Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/DEA-2021-13-03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/DEA-2021-13-03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Multiple solutions to a third-order three-point nonhomogeneous boundary value problem aided by nonlinear programming methods
. In this work, we consider a third order equation of three points with non-homogeneous conditions at the border. We apply Avery Peterson’s theorem, and present a theoretical result that guarantees the existence of multiple solutions to this problem under certain conditions. In addition, we present non-trivial examples and a new numerical method based on optimization is introduced.
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