Pietro d'Avenia

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.

On fractional Choquard equations

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.

ON THE LOGARITHMIC SCHRÖDINGER EQUATION

In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic equations with logarithmic nonlinearity arising in physically relevant situations. Furthermore, we prove that there exists a unique positive solution which is radially symmetric and nondegenerate.

Soliton dynamics for the Schrödinger-Newton system

We investigate the soliton dynamics for the Schrodinger-Newton system by proving a suitable modulational stability estimates in the spirit of those obtained by Weinstein for local equations.

Nonautonomous Klein–Gordon–Maxwell systems in a bounded domain

Abstract This paper deals with the Klein–Gordon–Maxwell system in a bounded spatial domain with a nonuniform coupling. We discuss the existence of standing waves in equilibrium with a purely electrostatic field, assuming homogeneous Dirichlet boundary conditions on the matter field and nonhomogeneous Neumann boundary conditions on the electric potential. Under suitable conditions we prove existence and nonexistence results. Since the system is variational, we use Ljusternik–Schnirelmann theory.