Positive solutions for double singularly perturbed Schrödinger Maxwell systems. (September 2018) - Ghimenti, Marco; Micheletti, Anna Maria
Abstract: We show that the number of solutions of a double singularly perturbed Schrödinger Maxwell system on a smooth bounded domain Ω ⊂ R 3 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.