Multiple Solitary Waves For a Non-homogeneous Schrödinger–Maxwell System in ℝ ³

Abstract

Abstract 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.