The uniqueness of symmetric single peak solutions for a Neumann problem involving critical exponent.
type: Item
instance of: scholarly article
title: The uniqueness of symmetric single peak solutions for a Neumann problem involving critical exponent.
zbMATH Open document ID: 1039.35040
author: Shuangjie Peng
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-02-03T00:00:00Z
review text: Let \(\Omega\) be a smooth bounded domain in \({\mathbb R}^N\), \(N\geq 5\). This paper is devoted to the semilinear Neumann boundary value problem \(-\Delta u+\lambda u=u^{2^*-1}+au^{q-1}\) in \(\Omega\), \(u>0\) in \(\Omega\), \(\partial u/\partial\nu =0\) on \(\partial\Omega\), where: \(\lambda>0\) is a large constant, \(a\) is a fixed positive constant, \(2^*=2N/(N-2)\) denotes the critical Sobolev exponent, and \(2<q<2^*\). The main result of the paper establishes the existence of a unique symmetric single peak solution. The proof is based on a constructive method and adequate elliptic estimates.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2037217
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: critical point theory
zbMATH Keywords: Neumann problem
zbMATH Keywords: critical Sobolev exponent
zbMATH Keywords: symmetric single peak solution
reviewed by: Vicenţiu D. Rădulescu
MaRDI profile type: Publication
full work available at URL: j.na.2003.08.003
OpenAlex ID: W2080152161
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DOI: 10.1016/J.NA.2003.08.003
description: scientific article; zbMATH DE number 2037217