Constant sign solutions for variable exponent system Neumann boundary value problems with singular coefficient
type: Item
instance of: scholarly article
title: Constant sign solutions for variable exponent system Neumann boundary value problems with singular coefficient
zbMATH Open document ID: 1470.35159
DOI: 10.1155/2014/396704
author: Xianbin Wu
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We deal with the existence of constant sign solutions for the following variable exponent system Neumann boundary value problem: \(- \text{div}(| \nabla u |^{p(x) - 2} \nabla u) + \lambda | u |^{p(x) - 2} u = F_u(x, u, v)\) in \(\Omega, - \text{div}(| \nabla v |^{q(x) - 2} \nabla v) + \lambda | v |^{q(x) - 2} v = F_v(x, u, v)\) in \(\Omega, \partial u / \partial \gamma = 0 = \partial v / \partial \gamma\) on \(\partial \Omega\). We give several sufficient conditions for the existence of the constant sign solutions, when \(F(x, \cdot, \cdot)\) satisfies neither sub-(\(p(x), q(x)\)) growth condition, nor Ambrosetti-Rabinowitz condition (subcritical). In particular, we obtain the existence of eight constant sign solutions.
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 35J50
Mathematics Subject Classification ID: 35J62
zbMATH DE Number: 7022309
Wikidata QID: Q59037310
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/396704
OpenAlex ID: W2014029198
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description: scientific article; zbMATH DE number 7022309