Positive solutions for double singularly perturbed Schrödinger Maxwell systems

We show that the number of solutions of a double singularly perturbed Schrödinger Maxwell system on a smooth bounded domain Ω⊂R3 depends on the topological properties of the domain. In particular if Ω is non contractible we obtain cat(Ω)+1 positive solutions. The result is obtained via Lusternik-Schnirelmann category theory.