Existence and Asymptotic Behavior of Positive Solutions for Variable Exponent Elliptic Systems  

作　　者：Honghui Yin Zuodong Yang 

机构地区：[1]School of Mathematical Sciences,Huaiyin Normal University,Jiangsu 223001,China [2]School of Teacher Education,Nanjing Normal University,Nanjing 210097,China [3]Institute of Mathematics,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China

出　　处：《Advances in Applied Mathematics and Mechanics》2016年第1期19-36,共18页应用数学与力学进展（英文）

基　　金：supported by the National Natural Science Foundation of China(No.11171092 and No.11471164);the Natural Science Foundation of Jiangsu Education Office(No.12KJB110002).

摘　　要：In this paper,our main purpose is to establish the existence of positive solution of the following system{−△ p(x)u=F(x,u,v),x∈W,−D q(x)v=H(x,u,v),x∈W,u=v=0,x∈∂W,where W=B(0,r)⊂RN or W=B(0,r2)\B(0,r1)⊂RN,0<r,0<r1<r2 are constants.F(x,u,v)=λp(x)[g(x)a(u)+f(v)],H(x,u,v)=θq(x)[g1(x)b(v)+h(u)],λ,θ>0 are parameters,p(x),q(x)are radial symmetric functions,−D p(x)=−div(|∇u|p(x)−2∇u)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.

关 键 词：Positive solution p(x)-Laplacian asymptotic behavior SUB-SUPERSOLUTION 

分 类 号：O17[理学—数学]