On Bound States Concentrating on Spheres for the Maxwell-Schrödinger Equation

We study the semiclassical limit for the following system of Maxwell-Schrr odinger equations: waves for the nonlinear Schrr odinger equation interacting with the electrostatic eld: the unknowns v and represent the wave function associated to the particle and the electric potential respectively. By using localized energy method, we construct a family of positive radially symmetric bound states (v ~ ; ~) such that v ~ concentrates around a sphere fjxj = s 0 g when ~ ! 0.