We look for standing waves of nonlinear Schrödinger equation coupled with Maxwell’s equations. We use the variational formulation introduced by Benci and Fortunato in 1992 for studying an eigenvalue problem for the Schrödinger-Maxwell system in bounded domains. We establish the existence of multiple standing waves both in the homogeneous and the non-homogeneous cases by means of the fibering method introduced by Pohozaev.

We look for solutions of a nonlinear perturbed Schrödinger equation with nonhomogeneous Dirichlet boundary conditions. By using a perturbation method introduced by Bolle, we prove the existence of multiple solutions in spite of the lack of the symmetry of the problem.