Annali di Matematica Pura ed Applicata

, Volume 190, Issue 3, pp 507–523

Multiple critical points for a class of nonlinear functionals

Article

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.

Keywords

Multiplicity result Nonlinear Schrödinger–Maxwell system Nonlinear elliptic Kirchhoff equation 

Mathematics Subject Classification (2000)

58E50 58E05 35J20 35J60 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica ed InformaticaUniversità degli Studi della BasilicataPotenzaItaly
  2. 2.Dipartimento di MatematicaPolitecnico di BariBariItaly

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