A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems
type: Item
instance of: scholarly article
title: A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems
zbMATH Open document ID: 0823.35064
author: Marco A. Souto
published in: Differential and Integral Equations
publication date: 1995-06-13T00:00:00Z
review text: The author deals with the existence of positive solutions for the system \(-\Delta u= M(x)u+ N(x,u)\) in \(\Omega\), \(u=0\) on \(\partial \Omega\), where \(\Omega \subset \mathbb{R}^ N\), \(N\geq 2\), is a regular bounded domain, \(u= (u_ 1, u_ 2)\), \(M(x)= (m_{ij} (x))\) is a \(2\times 2\) matrix with \(m_{ij} (x)\geq 0\), for all \(x\in \Omega\), \(i\neq j\) and \(N(x,u)= (f(x,u), g(x,u))\) when \(f\) has asymptotic behavior at \(+\infty\) as \(u^ \sigma_ 1\) and \(g\) satisfies some subcritical growth. The proofs are based on a known fixed point theorem in conical shells and the a priori bounds technique.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J50
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 763464
zbMATH Keywords: nonlinear elliptic systems
zbMATH Keywords: fixed point theorem in conical shells
reviewed by: Radu Precup
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 763464