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In this paper we study the existence of ground state solution and concentration of maxima for a class of strongly indefinite problem like\begin{document}$   \begin{cases} -\Delta u+V(x)u = A(\epsilon x)f(u) \quad \mbox{in} \quad   \mathbb{R}^{N}, \\ u\in H^{1}( \mathbb{R}^{N}), \end{cases} \qquad\qquad\qquad{(P)_{\epsilon}}   $\end{document}where   \begin{document}$ N \geq 1 $\end{document}  ,   \begin{document}$ \epsilon $\end{document}   is a positive parameter,   \begin{document}$ f: \mathbb{R} \to \mathbb{R} $\end{document}   is a continuous function with subcritical growth and   \begin{document}$ V,A: \mathbb{R}^{N} \to \mathbb{R} $\end{document}   are continuous functions verifying some technical conditions. Here   \begin{document}$ V $\end{document}   is a   \begin{document}$ \mathbb{Z}^N $\end{document}  -periodic function,   \begin{document}$ 0 \not\in \sigma(-\Delta + V) $\end{document}  , the spectrum of   \begin{document}$ -\Delta +V $\end{document}  , and\begin{document}$   0

Existence of ground state solution and concentration of maxima for a class of indefinite variational problems