Concentration and compactness in nonlinear Schrodinger-Poisson system with a general nonlinearity

TL;DR

This paper proves the existence of nonradial solutions to the nonlinear Schrödinger-Poisson system in three dimensions using concentration-compactness methods under general nonlinear assumptions.

Contribution

It introduces a novel application of concentration-compactness to establish solutions with minimal symmetry assumptions for a broad class of nonlinearities.

Findings

Existence of nontrivial nonradial solutions in R3

Application of concentration-compactness in Schrödinger-Poisson systems

Results hold under general nonlinear hypotheses

Abstract

In this paper we use a concentration and compactness argument to prove the existence of a nontrivial nonradial solution to the nonlinear Schrodinger-Poisson equations in R3, assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions