Low energy solutions for the semiclassical limit of Schroedinger Maxwell systems

TL;DR

This paper investigates how the number of solutions to the Schroedinger-Maxwell system in a bounded domain relates to the domain's topological features, using tools like Lusternik-Schnirelmann category and Poincaré polynomial.

Contribution

It establishes a link between the solutions of the Schroedinger-Maxwell system and the topological invariants of the domain, providing new insights into solution multiplicity.

Findings

Number of solutions depends on domain topology

Lusternik-Schnirelmann category influences solution count

Poincaré polynomial relates to solution multiplicity

Abstract

We show that the number of solutions of Schroedinger Maxwell system on a smooth bounded domain in R^3 depends on the topological properties of the domain. In particular we consider the Lusternik-Schnirelmann category and the Poincar\'e polynomial of the domain.