Ground states of Schrödinger systems with the Chern-Simons gauge fields

We are concerned with the following coupled nonlinear Schrödinger system: [equaction presented]. where ω, b > 0, p > 1. By virtue of the variational approach, we show the existence of nontrivial ground-state solutions depending on the parameters involved. Precisely, the aforementioned system admits a positive ground-state solution if p > 3 and b > 0 large enough or if p ∈ (2, 3 ] and b > 0 small.