Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential

Abstract

In this paper we consider the system in ${\mathbb{R}}^3$

for $p\in (1,5)$. We prove the existence of multi-bump solutions whose bumps concentrate around a local minimum of the potential $V(x)$. We point out that such solutions do not exist in the framework of the usual Nonlinear Schrödinger Equation.