Multiple $\mathbb{S}^{1}$-orbits for the Schr\"odinger-Newton system

TL;DR

This paper proves the existence and multiplicity of symmetric solutions to the Schrödinger-Newton system in three dimensions by applying equivariant Morse theory, advancing understanding of solutions' symmetry properties.

Contribution

It introduces a novel application of equivariant Morse theory to establish multiple symmetric solutions for the Schrödinger-Newton system.

Findings

Existence of symmetric solutions proven.

Multiple solutions identified.

Application of equivariant Morse theory demonstrated.

Abstract

We prove existence and multiplicity of symmetric solutions for the \emph{Schr\"odinger-Newton system} in three dimensional space using equivariant Morse theory.