Local mountain pass for a class of elliptic system

In this paper we are concerned with the existence and concentration of positive solutions for the following class of elliptic system(S){−ϵ2Δu+W(x)u=Qu(u,v)inRN,−ϵ2Δv+V(x)v=Qv(u,v)inRN,u(x),v(x)→0as|x|→∞,u,v>0inRN, where V, W are nonnegative Hölder continuous functions and Q is a p  -homogeneous function with 2