A note on solutions for asymptotically linear elliptic systems

Abstract

In this paper, we are concerned with the elliptic system of $$ \left\{ {\begin{array}{*{20}c} { - \Delta u + V(x)u = g(x,v), x \in R^N ,} \\ { - \Delta v + V(x)v = f(x,u), x \in R^N ,} \\ \end{array} } \right. $$ where V (x) is a continuous potential well, ƒ, g are continuous and asymptotically linear as t → ∞. The existence of a positive solution and ground state solution are established via variational methods.