Existence and multiplicity of positive solutions of semilinear elliptic equations in unbounded domains
type: Item
instance of: scholarly article
title: Existence and multiplicity of positive solutions of semilinear elliptic equations in unbounded domains
zbMATH Open document ID: 1226.35036
author: Kai Hu
author: Chun-Lei Tang
published in: Journal of Differential Equations
publication date: 2011-07-07T00:00:00Z
review text: The paper deals with semilinear elliptic equations of the following form \[ -\Delta u+u= Q(x) |u|^{p-2}u \] in an exterior domain of \(\mathbb R^N\). The authors give some existence and multiplicity results for positive solutions when the potential \(Q(x)\) is bounded, tends to a positive constant at infinity and may change sign. The methods are based on the investigation of the interaction of \(Q\) and on the properties of the topology of exterior domains very close to \(\mathbb R^N\).
reviewed by: Elvira Mascolo
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 5918266
zbMATH Keywords: elliptic equation
zbMATH Keywords: positive solution
zbMATH Keywords: exterior domain
zbMATH Keywords: lack of compactness
zbMATH Keywords: reduction method
zbMATH Keywords: linking
MaRDI profile type: Publication
full work available at URL: j.jde.2011.05.004
OpenAlex ID: W2003130064
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DOI: 10.1016/J.JDE.2011.05.004
description: scientific article; zbMATH DE number 5918266