Positive energy static solutions for the Chern-Simons-Schr\"odinger system under a large-distance fall-off requirement on the gauge potentials

TL;DR

This paper proves the existence of positive energy static solutions for the Chern-Simons-Schrödinger system with specific fall-off conditions on gauge potentials, and explores ground state solutions.

Contribution

It establishes the existence of static solutions with positive energy under large-distance fall-off conditions, a novel result for this system.

Findings

Existence of positive energy static solutions.

Conditions on gauge potentials at large distances.

Analysis of ground state solutions.

Abstract

In this paper we prove the existence of a positive energy static solution for the Chern-Simons-Schr\"odinger system under a large-distance fall-off requirement on the gauge potentials. We are also interested in existence of ground state solutions.