Four positive solutions of semilinear elliptic equations in exterior domains
type: Item
instance of: scholarly article
title: Four positive solutions of semilinear elliptic equations in exterior domains
zbMATH Open document ID: 1143.35047
author: Hwai-Chiuan Wang
author: Huei-Li Lin
author: Tsung-Fang Wu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-06-06T00:00:00Z
review text: The authors consider the semilinear elliptic equation \[ \begin{gathered} -\Delta_x u+ u= |u|^{p-2} u+ h(z)\quad\text{in }\Omega,\\ u\in H^1_0(\Omega),\end{gathered}\tag{1} \] where \(\Omega= \mathbb{R}^N\setminus\overline{\mathbb{D}}\), \(\mathbb{D}\) is a \(C^{1,1}\) bounded domain in \(\mathbb{R}^N\), \(2< p< 2^*\), \(2^*= {2N\over N-2}\) for \(N\geq 3\). Assuming that \(h\) is nonnegative and \(\| h\|_{L^2}> 0\), they prove that if \(\| h\|_{L^2}\) is sufficiently small, then there exist at least four positive solutions of (1).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 49J35
zbMATH DE Number: 5161913
zbMATH Keywords: positive solutions
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: minimax method
MaRDI profile type: Publication
full work available at URL: j.na.2006.07.001
OpenAlex ID: W1982620866
cites work: Four positive solutions for the semilinear elliptic equation: \(-\Delta u+u=a(x) u^p +f(x)\) in \(\mathbb{R}^N\)
cites work: Existence of positive solutions for a class of nonhomogeneous elliptic equations in \({\mathbb R}^N\)
cites work: Critical points and nonlinear variational problems
cites work: On a min-max procedure for the existence of a positive solution for certain scalar field equations in \({\mathbb{R}}^ N\)
cites work: On the existence of a positive solution of semilinear elliptic equations in unbounded domains
cites work: Symmetry of positive solutions of semilinear elliptic equations in infinite strip domains
cites work: A Necessary and Sufficient Condition for Palais--Smale Conditions
cites work: Multiple positive solutions of nonhomogeneous semilinear elliptic equations in ℝN
cites work: Existence of entire positive solutions for nonhomogeneous elliptic equations
cites work: A perturbation result of semilinear elliptic equations in exterior strip domains
cites work: Two positive solutions for a class of nonhomogeneous elliptic equations
cites work: Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
cites work: Existence of solutions of semilinear elliptic problems on unbounded domains
cites work: Q3749777
cites work: On nonhomogeneous elliptic equations involving critical Sobolev exponent
cites work: A Palais-Smale approach to problems in Esteban-Lions domains with holes
cites work: Symmetry breaking in a bounded symmetry domain
cites work: A perturbation result on positive entire solutions of a semilinear elliptic equation
cites work: Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains
DOI: 10.1016/J.NA.2006.07.001
description: scientific article; zbMATH DE number 5161913