A multiplicity result for a double perturbed Schr\"odinger-Bopp-Podolsky-Proca system

TL;DR

This paper proves that the number of solutions to a double perturbed Schrödinger-Bopp-Podolsky-Proca system on a compact 3D manifold is related to the manifold's topology, using Lusternik-Schnirelmann category theory.

Contribution

It establishes a new multiplicity result linking solution count to topological invariants for this specific PDE system.

Findings

Number of solutions depends on the manifold's topology

Uses Lusternik-Schnirelmann category to establish multiplicity

Results apply to a class of perturbed Schrödinger systems

Abstract

In this paper we will prove a multiplicity result for a double perturbed Schr\"odinger-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.