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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

Honghui Yin  and
Zuodong Yang
Honghui Yin
Affiliation:
School of Mathematical Sciences, Huaiyin Normal University, Jiangsu 223001, China
Zuodong Yang*
Affiliation:
School of Teacher Education, Nanjing Normal University, Nanjing 210097, China Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
*
*Corresponding author. Email:yinhh@hytc.edu.cn (H. H. Yin), zdyang_jin@263.net (Z. D. Yang)
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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.

Keywords

35J6035J62Positive solutionp(x)-Laplacianasymptotic behaviorsub-supersolution
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 1 , February 2016 , pp. 19 - 36
Copyright
Copyright © Global-Science Press 2016 

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