奇异超线性方程外域上变符号解的存在性与不存在性

IF 1 3区数学 Q1 MATHEMATICS

Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI:10.3934/cpaa.2023107

Joseph Iaia

{"title":"奇异超线性方程外域上变符号解的存在性与不存在性","authors":"Joseph Iaia","doi":"10.3934/cpaa.2023107","DOIUrl":null,"url":null,"abstract":"In this paper we study radial solutions of $ \\Delta u + K(|x|) f(u) = 0 $ in the exterior of the ball of radius $ R>0 $ in $ {\\mathbb R}^{N} $ where $ f $ grows superlinearly at infinity and is singular at $ 0 $ with $ f(u) \\sim -\\frac{1}{|u|^{q-1}u} $ and $ 0<q<1 $ for small $ u $. We assume $ K(|x|) \\sim |x|^{-\\alpha} $ for large $ |x| $ and establish existence of an infinite number of sign-changing solutions when $ N+q(N-2) <\\alpha <2(N-1). $ We also prove nonexistence for $ 0<\\alpha < N+ q(N-2) $.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"33 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and nonexistence of sign-changing solutions for singular superlinear equations on exterior domains\",\"authors\":\"Joseph Iaia\",\"doi\":\"10.3934/cpaa.2023107\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we study radial solutions of $ \\\\Delta u + K(|x|) f(u) = 0 $ in the exterior of the ball of radius $ R>0 $ in $ {\\\\mathbb R}^{N} $ where $ f $ grows superlinearly at infinity and is singular at $ 0 $ with $ f(u) \\\\sim -\\\\frac{1}{|u|^{q-1}u} $ and $ 0<q<1 $ for small $ u $. We assume $ K(|x|) \\\\sim |x|^{-\\\\alpha} $ for large $ |x| $ and establish existence of an infinite number of sign-changing solutions when $ N+q(N-2) <\\\\alpha <2(N-1). $ We also prove nonexistence for $ 0<\\\\alpha < N+ q(N-2) $.\",\"PeriodicalId\":10643,\"journal\":{\"name\":\"Communications on Pure and Applied Analysis\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications on Pure and Applied Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/cpaa.2023107\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure and Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/cpaa.2023107","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了$ {\mathbb R}^{N} $中半径为$ R>0 $的球外$ \Delta u + K(|x|) f(u) = 0 $的径向解，其中$ f $在无穷远处超线性增长，在$ 0 $处奇异，对于小的$ u $有$ f(u) \sim -\frac{1}{|u|^{q-1}u} $和$ 0<q<1 $。对于较大的$ |x| $，我们假设为$ K(|x|) \sim |x|^{-\alpha} $，当$ N+q(N-2) <\alpha <2(N-1). $时，我们证明了无穷多个变号解的存在性。对于$ 0<\alpha < N+ q(N-2) $，我们也证明了不存在性。

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

Existence and nonexistence of sign-changing solutions for singular superlinear equations on exterior domains

In this paper we study radial solutions of $ \Delta u + K(|x|) f(u) = 0 $ in the exterior of the ball of radius $ R>0 $ in $ {\mathbb R}^{N} $ where $ f $ grows superlinearly at infinity and is singular at $ 0 $ with $ f(u) \sim -\frac{1}{|u|^{q-1}u} $ and $ 0

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

Communications on Pure and Applied Analysis 数学-数学

CiteScore

1.90

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.

京公网安备 11010802042870号

Book学术文献互助群
群号：481959085