Large positive solutions of semilinear elliptic equations with critical and supercritical growth
type: Item
instance of: scholarly article
title: Large positive solutions of semilinear elliptic equations with critical and supercritical growth
zbMATH Open document ID: 1013.35039
DOI: 10.1016/S0022-247X(02)00054-9
author: Zongming Guo
author: Hui Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-09-17T00:00:00Z
review text: The authors study large positive solutions of the problem \[ \begin{cases} -\Delta u=u^p- \varepsilon u^q\quad &\text{in }\Omega\\ u=0\quad &\text{on }\Omega,\end{cases} \tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N (N \geq 3)\) with smooth boundary \(\partial\Omega\) and \(q>p\geq p_N:= {N+2\over N-2}\), \(\varepsilon>0\). They obtain existence and uniqueness of large positive solutions for (1) and study their asymptotic behaviour as \(\varepsilon \to 0\). It is shown that they develop a boundary layer and the boundary derivative estimate of the large solution is also established.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1801635
zbMATH Keywords: large positive solutions
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: critical and supercritical growth
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: boundary derivative estimate
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00054-9
OpenAlex ID: W2014323824
description: scientific article; zbMATH DE number 1801635