Ground state solutions for a diffusion system

In this paper, we study the following diffusion system {∂tu−Δxu+V(x)u=g(t,x,v),−∂tv−Δxv+V(x)v=f(t,x,u) where z:=(u,v):R×RN→R2z:=(u,v):R×RN→R2, V(x)∈C(RN,R)V(x)∈C(RN,R) is a general periodic function. Under weaker conditions on nonlinearity, we establish the existence of ground state solutions via variational methods.