Standing waves of modified Schr\"odinger equations coupled with the Chern-Simons gauge theory

TL;DR

This paper investigates standing wave solutions of a modified Schrödinger equation coupled with Chern-Simons gauge theory, establishing existence and non-existence results through variational methods.

Contribution

It introduces a novel application of Nehari-Pohozaev constraint minimization to prove existence of radial ground states in this coupled system.

Findings

Existence of radial ground state solutions

Non-existence of nontrivial solutions under certain conditions

Application of variational methods to coupled Schrödinger-Chern-Simons system

Abstract

We are interested in standing waves of a modified Schr\"odinger equation coupled with the Chern-Simons gauge theory. By applying a constraint minimization of Nehari-Pohozaev type, we prove the existence of radial ground state solutions. We also investigate the non-existence for nontrivial solutions.