Standing waves for 6-superlinear Chern-Simons-Schrödinger systems with indefinite potentials

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