Ground state solution for a class of indefinite variational problems with critical growth

In this paper we study the existence of ground state solution for an indefinite variational problem of the type(P){−Δu+(V(x)−W(x))u=f(x,u)inRN,u∈H1(RN), where N≥2, V,W:RN→R and f:RN×R→R are continuous functions verifying some technical conditions and f possesses a critical growth. Here, we will consider the case where the problem is asymptotically periodic, that is, V is ZN-periodic, W goes to 0 at infinity and f is asymptotically periodic.