Multiple critical points for a class of nonlinear functionals

Abstract

In this paper, we prove a multiplicity result concerning the critical points of a class of functionals involving local and nonlocal nonlinearities. We apply our result to the nonlinear Schrödinger–Maxwell system in \({\mathbb{R}^3}\) and to the nonlinear elliptic Kirchhoff equation in \({\mathbb{R}^N}\) assuming on the local nonlinearity the general hypotheses introduced by Berestycki and Lions.