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

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
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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
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奇异超线性方程外域上变符号解的存在性与不存在性
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。
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来源期刊
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.
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