Existence and uniqueness of positive solutions to the boundary blow-up problem for an elliptic system
type: Item
instance of: scholarly article
title: Existence and uniqueness of positive solutions to the boundary blow-up problem for an elliptic system
zbMATH Open document ID: 1220.35039
author: Mingxin Wang
author: Huiling Li
published in: Journal of Differential Equations
publication date: 2007-03-12T00:00:00Z
review text: The authors deal with a system of semilinear elliptic equation of the form \[ \begin{gathered} -\Delta u= u(a_1- b_1 u^m- c_1 v^n),\quad x\in\Omega,\\ -\Delta v= v(a_2- b_2 u^p- c_2 v^q),\quad x\in\Omega,\end{gathered}\tag{1} \] where \(\Omega\subset\mathbb{R}^d\) is a bounded domain of class \(C^{2,\alpha}\) for some \(\alpha\in (0,1)\). The main goal of this paper is to study the influence of the parameters \(a_i\), \(b_i\), \(c_i\) \((i= 1,2)\) and the exponents \(m\), \(n\), \(p\), \(q\) on the existence, uniqueness and asymptotic behaviour of positive solutions to the system (1) under different boundary conditions.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 5132874
zbMATH Keywords: boundary blow-up problem
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: boundary behavior
MaRDI profile type: Publication
full work available at URL: j.jde.2006.11.003
OpenAlex ID: W1984210911
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DOI: 10.1016/J.JDE.2006.11.003
description: scientific article; zbMATH DE number 5132874