Solutions of the Schrödinger-Poisson problem concentrating on spheres. II. Existence

The SchroedingerPoisson system describes standing waves for the nonlinear Schroedinger equation interacting with the electrostatic field. We deal with the semiclassical states for this system and prove the existence of radial solutions concentrating on spheres in the presence of an external potential and with a non-constant density charge. In particular, we show that the necessary conditions obtained in Part I are also sufficient if suitable non-degeneracy conditions are assumed. We use a perturbation technique in a variational setting.