Existence and concentration of positive bound states for the Schr\"odinger-Poisson system with potentials

Abstract

In this article we study the existence and concentration behavior of bound states for a nonlinear Schr\"odinger-Poisson system with a parameter $\varepsilon>0$. Under some suitable conditions on the potential functions, we prove that for $\varepsilon$ small the system has a positive solution that concentrates at a point which is a global minimum of the minimax function associated to the related autonomous problem.