In this paper we study the existence of ground state solution for an indefinite variational problem of the type $$ \left\{ \begin{ array}{ l} -\Delta u+(V(x)-W(x))u=f(x,u) \quad \mbox{ in} \quad \R^{ N}, u\in H^{ 1}(\R^{ N}), \end{ array}\right. \eqno{ (P)} $$ where $N \geq 2$, $V,W:\mathbb{ R}^N \to \mathbb{ R}$ and $f:\mathbb{ R}^N \times \mathbb{ R} \to \mathbb{ R}$ 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 $\mathbb{ Z}^N$-periodic, $W$ goes to 0 at infinity and $f$ is asymptotically periodic.
Categories: math.AP