Existence results for a non-relativistic Chern-Simons model with purely mutual interaction

TL;DR

This paper proves the existence and multiplicity of solutions for a non-relativistic Chern-Simons model involving a singular Liouville system, overcoming variational challenges with Morse theory.

Contribution

It introduces a novel constrained variational approach and Morse-theoretical methods to handle an indefinite energy functional in the Chern-Simons Liouville system.

Findings

Established existence of solutions

Proved multiplicity of solutions

Developed a new variational framework for indefinite problems

Abstract

We are concerned with a skew-symmetric singular Liouville system arising in non-relativistic Chern-Simons theory. Based on its variational structure, we establish existence and multiplicity results. Since the energy functional is indefinite, standard variational approaches do not apply directly. We overcome this difficulty by introducing a suitable constrained problem and implementing a Morse-theoretical argument