Asymptotic behavior of positive solutions of some elliptic problems.
type: Item
instance of: scholarly article
title: Asymptotic behavior of positive solutions of some elliptic problems.
zbMATH Open document ID: 1094.35045
author: Yihong Du
author: E. N. Dancer
author: Li Ma
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: The authors deal with the asymptotic behavior of positive solutions of the problem \[ \begin{cases} -\Delta u=au-b(x)u^p,\quad & x\in\Omega\\ u=0, \quad &\text{on }\partial\Omega,\end{cases}\tag{1} \] for \(p\) near 1 and near \(\infty\), respectively. Here \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^N\) \((N\geq 1)\) and \(b(x)\) is a nonnegative function in \(C (\overline\Omega)\), \(a\) and \(p\) are constants but the exponent \(p\) is always greater than 1. The authors show that, for each case, the behavior is determined by a limiting problem. Moreover, the limiting problem is of free boundary nature when \(p\to\infty\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B20
zbMATH DE Number: 2101086
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: pjm.2003.210.215
OpenAlex ID: W2058564126
DOI: 10.2140/PJM.2003.210.215
description: scientific article; zbMATH DE number 2101086