Standing waves for 6-superlinear Chern-Simons-Schr\"{o}dinger systems with indefinite potentials

TL;DR

This paper investigates 6-superlinear Chern-Simons-Schrödinger systems with indefinite potentials, employing Morse theory to establish the existence of nontrivial solutions in a novel setting where the potential is not definitively positive or negative.

Contribution

It introduces an analysis of Chern-Simons-Schrödinger systems with indefinite potentials, a case less explored in prior research, and applies Morse theory to find solutions.

Findings

Existence of nontrivial solutions for the system.

Application of Morse theory in indefinite potential setting.

Handling of finite-dimensional negative space in the Schrödinger operator.

Abstract

In this paper we consider 6-superlinear Chern-Simons-Schr\"{o}dinger systems. In contrast to most studies, we consider the case where the potential $V$ is indefinite so that the Schr\"{o}dinger operator $-\Delta +V$ possesses a finite-dimensional negative space. We obtain nontrivial solutions for the problem via Morse theory.