Uniqueness and existence of positive solutions for some semilinear elliptic systems
type: Item
instance of: scholarly article
title: Uniqueness and existence of positive solutions for some semilinear elliptic systems
zbMATH Open document ID: 1113.35061
author: Masaaki Maniwa
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-11-26T00:00:00Z
review text: The author deals with positive solutions of the following semilinear elliptic system \[ \begin{cases} -\Delta u_i= \prod^N_{j=1} u^{p_{ij}}_j\quad &\text{in }\Omega,\\ u_i= 0\quad &\text{on }\partial\Omega,\quad i= 1,2,\dots, N,\end{cases}\tag{1} \] where \(p_{ij}\) \((1\leq i,\;j\leq N)\) are nonnegative constants and \(\Omega\subset\mathbb{R}^n\) \((n\geq 1)\) denotes a bounded domain of class \(C^{2,\alpha}\), \(\alpha\in (0,1)\). The author shows the uniqueness and existence of positive solutions for (1). To this end, he uses a concept of the M-matrix.
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 2119151
zbMATH Keywords: Semilinear elliptic system
zbMATH Keywords: Positive solution
zbMATH Keywords: M-matrix
zbMATH Keywords: Existence
zbMATH Keywords: Uniqueness
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.na.2004.08.006
OpenAlex ID: W2131835746
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DOI: 10.1016/J.NA.2004.08.006
description: scientific article; zbMATH DE number 2119151