Multiplicity of positive solutions for semilinear elliptic systems
type: Item
instance of: scholarly article
title: Multiplicity of positive solutions for semilinear elliptic systems
zbMATH Open document ID: 1277.35161
DOI: 10.1155/2013/746380
author: Tsing-San Hsu
published in: Abstract and Applied Analysis
publication date: 2013-09-19T00:00:00Z
review text: Summary: We study the effect of the coefficient \(h(x)\) of the critical nonlinearity on the number of positive solutions for semilinear elliptic systems. Under suitable assumptions for \(f(x)\), \(g(x)\), and \(h(x)\), we prove that for sufficiently small \(\lambda, \mu > 0\), there are at least \(k + 1\) positive solutions of the semilinear elliptic systems \(-\Delta u = \lambda f(x)|u|^{q-2}u + (\alpha/(\alpha + \beta))h(x)|u|^{\alpha -2}u|v|^\beta\), \(-\Delta v = \mu g(x)|v|^{q-2}v + (\beta/(\alpha + \beta))h(x)|u|^\alpha|v|^{\beta-2}v\), where \(0 \in \Omega \subset \mathbb R^N\) is a bounded domain, \(\alpha > 1\), \(\beta > 1\), and \(N/(N - 2) < q < 2 < \alpha + \beta = 2^\ast\) for \(N > 4\).
Mathematics Subject Classification ID: 35J47
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 6209424
zbMATH Keywords: critical nonlinearity
zbMATH Keywords: positive solutions
zbMATH Keywords: semilinear elliptic systems
Wikidata QID: Q58917326
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/746380
OpenAlex ID: W2015338532
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description: scientific article; zbMATH DE number 6209424