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) ⎧⎪ ⎪⎨⎪ ⎪⎩ − 2 u +W(x)u =Qu(u, v) in RN, − 2 v +V (x)v =Qv(u, v) in RN, u(x), v(x)→0 as |x|→∞, u, v >0 in RN, where V ,W are nonnegative Hölder continuous functions andQis a p-homogeneous function with 2