On the existence of explosive solutions for semilinear elliptic problems
type: Item
instance of: scholarly article
title: On the existence of explosive solutions for semilinear elliptic problems
zbMATH Open document ID: 1033.35040
DOI: 10.1016/S0362-546X(00)00233-9
author: Zhijun Zhang
author: Shuangping Tao
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-03-08T00:00:00Z
review text: This paper deals with the model problem \[ \Delta u= k(x)f(u),\quad u> 0,\quad x\in\Omega,\quad u|_{\partial\Omega}= \infty,\tag{1} \] where \(\Omega\) is a domain in \(\mathbb{R}^N\) \((N> 2)\), and the functions \(k\) and \(f\) satisfy certain conditions. The authors extend the results of both Lair and Wood, Lazar and McKenna, and construct the lowest explosive subsolution of problem (1) with more general \(k(x)\) and \(f(s)\). In addition, when \(\Omega= \mathbb{R}^N\), the authors prove that problem (1) has an entire solution \(u\in C^2(\mathbb{R}^N)\) for more general \(f(s)\).
reviewed by: Zeng Yuesheng
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1741844
MaRDI profile type: Publication
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full work available at URL: s0362-546x(00)00233-9
OpenAlex ID: W2038143543
description: scientific article; zbMATH DE number 1741844