A multiplicity result for double singularly perturbed elliptic systems

TL;DR

This paper demonstrates that the quantity of low energy solutions for a double singularly perturbed Schrödinger-Maxwell system on a 3D manifold is related to the manifold's topological features, using Lusternik-Schnirelmann theory.

Contribution

It establishes a link between the number of solutions and the topological properties of the manifold for a specific class of elliptic systems.

Findings

Number of solutions depends on manifold topology

Uses Lusternik-Schnirelmann category theory

Provides a lower bound for solutions

Abstract

We show that the number of low energy solutions of a double singularly perturbed Schroedinger Maxwell system type on a smooth 3 dimensional manifold (M,g) depends on the topological properties of the manifold. The result is obtained via Lusternik Schnirelmann category theory.