Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient

Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient

We deal with the existence of constant sign solutions for the following variable exponent system Neumann boundary value problem: -div(|∇u|p(x)-2∇u)+λ|u|p(x)-2u=Fu(x,u,v)  in  Ω, -div(|∇v|q(x)-2∇v)+λ|v|q(x)-2v=Fv(x,u,v) in Ω, ∂u/∂γ=0=∂v/∂γ  on  ∂Ω. We give several sufficient conditions for the existe...

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Main Author: Xianbin Wu
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/396704
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spelling doaj-ba0ad574b33144c5a781be4648e3ebf72020-11-24T22:48:07ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/396704396704Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular CoefficientXianbin Wu0Junior College, Zhejiang Wanli University, Ningbo, Zhejiang 315100, ChinaWe deal with the existence of constant sign solutions for the following variable exponent system Neumann boundary value problem: -div(|∇u|p(x)-2∇u)+λ|u|p(x)-2u=Fu(x,u,v)  in  Ω, -div(|∇v|q(x)-2∇v)+λ|v|q(x)-2v=Fv(x,u,v) in Ω, ∂u/∂γ=0=∂v/∂γ  on  ∂Ω. We give several sufficient conditions for the existence of the constant sign solutions, when F(x,·,·) 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.http://dx.doi.org/10.1155/2014/396704
collection DOAJ
language English
format Article
sources DOAJ
author Xianbin Wu
spellingShingle Xianbin Wu
Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient
Abstract and Applied Analysis
author_facet Xianbin Wu
author_sort Xianbin Wu
title Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient
title_short Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient
title_full Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient
title_fullStr Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient
title_full_unstemmed Constant Sign Solutions for Variable Exponent System Neumann Boundary Value Problems with Singular Coefficient
title_sort constant sign solutions for variable exponent system neumann boundary value problems with singular coefficient
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We deal with the existence of constant sign solutions for the following variable exponent system Neumann boundary value problem: -div(|∇u|p(x)-2∇u)+λ|u|p(x)-2u=Fu(x,u,v)  in  Ω, -div(|∇v|q(x)-2∇v)+λ|v|q(x)-2v=Fv(x,u,v) in Ω, ∂u/∂γ=0=∂v/∂γ  on  ∂Ω. We give several sufficient conditions for the existence of the constant sign solutions, when F(x,·,·) 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.
url http://dx.doi.org/10.1155/2014/396704
work_keys_str_mv AT xianbinwu constantsignsolutionsforvariableexponentsystemneumannboundaryvalueproblemswithsingularcoefficient
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