Multiple critical points for a class of nonlinear functionals

TL;DR

This paper establishes multiple critical points for a class of nonlinear functionals with local and nonlocal terms, applying the results to Schrödinger-Maxwell and Kirchhoff equations under broad conditions.

Contribution

It introduces a new multiplicity theorem for critical points of nonlinear functionals with local and nonlocal nonlinearities, extending previous results.

Findings

Proves existence of multiple critical points for the class of functionals.

Applies the theoretical results to nonlinear Schrödinger-Maxwell system.

Extends the analysis to nonlinear elliptic Kirchhoff equations.

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 Schrodinger-Maxwell system and to the nonlinear elliptic Kirchhoff equation assuming on the local nonlinearity the general hypotheses introduced by Berestycki and Lions.