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Existence and Asymptotic Behavior of Positive Solutions for Variable Exponent Elliptic Systems
Published online by Cambridge University Press: 21 December 2015
Abstract
In this paper, our main purpose is to establish the existence of positive solution of the following system where are constants. F(x,u,υ) = λp(x)[g(x)a(u)+f(υ)], H(x,u,υ)=θq(x)[g1(x)b(υ)+h(u)], λ, θ>0 are parameters, p(x), q(x) are radial symmetric functions, is called p(x)-Laplacian. We give the existence results and consider the asymptotic behavior of the solutions. In particular, we do not assume any symmetric condition, and we do not assume any sign condition on F(x,0,0) and H(x,0,0) either.
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- Copyright © Global-Science Press 2016