Multiplicity of solutions of a zero mass nonlinear equation on a Riemannian manifold

TL;DR

This paper investigates how the number of solutions to a nonlinear equation on a Riemannian manifold relates to the manifold's topology, using topological methods like Ljusternik-Schnirelmann category and Morse theory.

Contribution

It introduces a topological approach to estimate the multiplicity of solutions for a zero mass nonlinear equation on Riemannian manifolds.

Findings

Number of solutions correlates with the manifold's topology.

Ljusternik-Schnirelmann category provides lower bounds for solutions.

Morse theory links critical points to solution multiplicity.

Abstract

The relation between the number of solutions of a nonlinear equation on a Riemannian manifold and the topology of the manifold itself is studied. The technique is based on Ljusternik-Schnirelmann category and Morse theory.