, Volume 190, Issue 3, pp 507-523
Date: 19 Aug 2010

Multiple critical points for a class of nonlinear functionals

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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.

The authors are supported by M.I.U.R.—P.R.I.N. “Metodi variazionali e topologici nello studio di fenomeni non lineari”.