Semi-classical states for Schrodinger-Poisson systems on R^3

In this article, we study the nonlinear Schrodinger-Poisson equation $$\displaylines{ -\epsilon^2\Delta u+V(x) u+\phi(x)u=f(u), \quad x\in{\mathbb{R}^3}, \cr -\epsilon^2\Delta\phi=u^2,\quad \lim_{|x|\to\infty}\phi(x)=0\,. }$$ Under suitable assumptions on V(x) and f(s), we prove the existence of ground state solution around local minima of the potential V(x) as $\epsilon\to 0$. Also, we show the exponential decay of ground state solution.