{"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}
引用次数: 0
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
期刊介绍:
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