Local mountain pass for a class of elliptic system

摘要

In this paper we are concerned with the existence and concentration of positive solutions for the following class of elliptic system (S) {-∈~2Δu + W(x)u = Q_u(u,v) in R~N, -∈~2Δv + V(x)v = Q_v(u,v) in R~N, u(x), v(x) → 0 as |x| → ∞, u, v > 0 in R~N, where V, W are nonnegative Holder continuous functions and Q is a p-homogeneous function with 2 < p < 2N/(N-2) for N ≥ 3.