具有不连续非线性的超线性椭圆问题的正解

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2021-01-01 DOI:10.1070/IM9000

V. Pavlenko, D. K. Potapov

{"title":"具有不连续非线性的超线性椭圆问题的正解","authors":"V. Pavlenko, D. K. Potapov","doi":"10.1070/IM9000","DOIUrl":null,"url":null,"abstract":"We consider an elliptic boundary-value problem with a homogeneous Dirichlet boundary condition, a parameter and a discontinuous non-linearity. The positive parameter appears as a multiplicative term in the non-linearity, and the problem has a zero solution for any value of the parameter. The non-linearity has superlinear growth at infinity. We prove the existence of positive solutions by a topological method.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"262 - 278"},"PeriodicalIF":0.8000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Positive solutions of superlinear elliptic problems with discontinuous non-linearities\",\"authors\":\"V. Pavlenko, D. K. Potapov\",\"doi\":\"10.1070/IM9000\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider an elliptic boundary-value problem with a homogeneous Dirichlet boundary condition, a parameter and a discontinuous non-linearity. The positive parameter appears as a multiplicative term in the non-linearity, and the problem has a zero solution for any value of the parameter. The non-linearity has superlinear growth at infinity. We prove the existence of positive solutions by a topological method.\",\"PeriodicalId\":54910,\"journal\":{\"name\":\"Izvestiya Mathematics\",\"volume\":\"85 1\",\"pages\":\"262 - 278\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1070/IM9000\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/IM9000","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

考虑一类具有齐次Dirichlet边界条件、参数和不连续非线性的椭圆型边值问题。正参数在非线性中以乘法项的形式出现，对于参数的任何值，问题都有一个零解。非线性在无穷远处有超线性增长。用拓扑方法证明了正解的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Positive solutions of superlinear elliptic problems with discontinuous non-linearities

We consider an elliptic boundary-value problem with a homogeneous Dirichlet boundary condition, a parameter and a discontinuous non-linearity. The positive parameter appears as a multiplicative term in the non-linearity, and the problem has a zero solution for any value of the parameter. The non-linearity has superlinear growth at infinity. We prove the existence of positive solutions by a topological method.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.