Multiplicity of single-bump solutions for semilinear elliptic equations in multi-bump domains
type: Item
instance of: scholarly article
title: Multiplicity of single-bump solutions for semilinear elliptic equations in multi-bump domains
zbMATH Open document ID: 1113.35076
author: Tsung-Fang Wu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-11-26T00:00:00Z
review text: The author studies the following semilinear elliptic equation \[ \begin{cases} -\Delta u+ u= |u|^{p-2}u\quad &\text{in }\Omega,\\ u= 0\quad &\text{on }\partial\Omega,\end{cases}\tag{1} \] where \(\Omega\) is a domain in \(\mathbb{R}^N\) and \(p\) satisfies \(p> 2\) if \(N= 2\) and \(2< p<{2N\over N-2}\) for \(N\geq 3\). The main goal of the author is to use the shape of the domain \(\Omega\) prove that (1) has multiple positive solutions.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2119150
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: Palais-Smale
zbMATH Keywords: multi-bump domains
zbMATH Keywords: multiple solutions
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.na.2004.07.045
OpenAlex ID: W2073310089
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DOI: 10.1016/J.NA.2004.07.045
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description: scientific article; zbMATH DE number 2119150