In this paper we study the existence of ground state solution and concentration of maxima for a class of strongly indefinite problem like $$ \left\{ \begin{ array}{ l} -\Delta u+V(x)u=A(\epsilon x)f(u) \quad \mbox{ in} \quad \R^{ N}, \\ u\in H^{ 1}(\R^{ N}), \end{ array}\right. \eqno{ (P)_{ \epsilon}} $$ where $N \geq 1$, $\epsilon$ is a positive parameter, $f: \mathbb{ R} \to \mathbb{ R}$ is a continuous function with subcritical growth and $V,A: \mathbb{ R}^{ N} \to \mathbb{ R}$ are continuous functions verifying some technical conditions. Here $V$ is a $\mathbb{ Z}^N$-periodic function, $0 \not\in \sigma(-\Delta + V)$, the spectrum of $-\Delta +V$, and $$ 0 < \inf_{ x \in \R^{ N}}A(x)\leq \displaystyle\lim_{ |x|\rightarrow+\infty}A(x)<\sup_{ x \in \R^{ N}}A(x). $$
Categories: math.AP