%0 Journal Article %J Mathematical Models and Methods in Applied Sciences %D 2009 %T Solutions of the Schrödinger–Poisson problem concentrating on spheres, part I: necessary conditions %A Ianni, Isabella %A Giusi Vaira %X

In this paper we study a coupled nonlinear Schrödinger–Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schrödinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

%B Mathematical Models and Methods in Applied Sciences %V 19 %P 707-720 %G eng %U https://doi.org/10.1142/S0218202509003589 %R 10.1142/S0218202509003589 %0 Journal Article %J Advanced nonlinear studies %D 2008 %T On concentration of positive bound states for the Schrödinger-Poisson problem with potentials %A Ianni, Isabella %A Giusi Vaira %X

We study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

%B Advanced nonlinear studies %I Advanced Nonlinear Studies, Inc. %V 8 %P 573–595 %G eng %R 10.1515/ans-2008-0305.