Ground states for diffusion system with periodic and asymptotically periodic nonlinearity

In this paper, we study the following diffusion system {∂tu−Δxu+b(t,x)⋅∇xu+V(x)u=g(t,x,v),−∂tv−Δxv−b(t,x)⋅∇xv+V(x)v=f(t,x,u) where b∈C1(R×RN,RN)b∈C1(R×RN,RN) and V(x)∈C(RN,R)V(x)∈C(RN,R). By using non-Nehari manifold method developed in Tang (2014), we investigate the existence of the ground state solutions of Nehari type for the above problem with periodic and asymptotically periodic nonlinearity.