Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields

We study the existence of standing waves for a class of nonlinear Schrödinger equations in ℝn, with both an electric and a magnetic field. Under suitable non-degeneracy assumptions on the critical points of an auxiliary function related to the electric field, we prove the existence and the multiplicity of complex-valued solutions in the semiclassical limit. We show that, in the semiclassical limit, the presence of a magnetic field produces a phase in the complex wave, but it does not influence the location of peaks of the modulus of these waves. © 2002 Elsevier Science (USA). All rights reserved.