SOLUTIONS OF THE SCHRÖDINGER–POISSON PROBLEM CONCENTRATING ON SPHERES, PART I: NECESSARY CONDITIONS
Isabella Ianni, Giusi Vaira · Mathematical Models and Methods in Applied Sciences · 2009
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.