Showing papers by "Antonio Azzollini published in 2010"

On the Schrödinger-Maxwell equations under the effect of a general nonlinear term

Abstract: In this paper we prove the existence of a nontrivial solution to the nonlinear Schrodinger–Maxwell equations in R 3 , assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions.

Ground state solutions for the nonlinear Klein-Gordon-Maxwell equations

Abstract: In this paper we prove the existence of a ground state solution for the nonlinear Klein–Gordon–Maxwell equations in the electrostatic case.

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

The elliptic Kirchhoff equation in $\R^N$ perturbed by a local nonlinearity

Abstract: In this paper we present a very simple proof of the existence of at least one non trivial solution for a Kirchhoff type equation on $\RN$, for $N\ge 3$. In particular, in the first part of the paper we are interested in studying the existence of a positive solution to the elliptic Kirchhoff equation under the effect of a nonlinearity satisfying the general Berestycki-Lions assumptions. In the second part we look for ground states using minimizing arguments on a suitable natural constraint.

Generalized Schrodinger-Poisson type systems

Abstract: In this paper we study some Schrodinger-Poisson type systems on a bounded domain, with Dirichlet boundary condition on both the variables.