{"title":"Resonant Sturm–Liouville Boundary Value Problems for Differential Systems in the Plane","authors":"A. Boscaggin, M. Garrione","doi":"10.4171/ZAA/1554","DOIUrl":null,"url":null,"abstract":"We study the Sturm-Liouville boundary value problem associated with the planar differential system Jz′ = ∇V (z) + R(t, z), where V (z) is positive and positively 2-homogeneous and R(t, z) is bounded. Assuming Landesman-Lazer type conditions, we obtain the existence of a solution in the resonant case. The proofs are performed via a shooting argument. Some applications to boundary value problems associated with scalar second order asymmetric equations are discussed. MSC 2010 Classification 34B15.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/ZAA/1554","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We study the Sturm-Liouville boundary value problem associated with the planar differential system Jz′ = ∇V (z) + R(t, z), where V (z) is positive and positively 2-homogeneous and R(t, z) is bounded. Assuming Landesman-Lazer type conditions, we obtain the existence of a solution in the resonant case. The proofs are performed via a shooting argument. Some applications to boundary value problems associated with scalar second order asymmetric equations are discussed. MSC 2010 Classification 34B15.
分享
京公网安备 11010802042870号
京ICP备2023020795号-1
求助内容：
应助结果提醒方式：
扫码关注我们
