A multiplicity result for a double perturbed Schrödinger-Bopp-Podolsky-Proca system

In this paper we will prove a multiplicity result for a double perturbed Schrödinger-Bopp- Podolsky-Proca system on a compact 3-dimensional Riemannian manifold without boundary. We will prove, using the Lusternik-Schnirelmann Category, that the number of solutions of the system depends on the topological properties of the manifold.