Ground states of fermionic nonlinear Schrödinger systems with Coulomb potential I: the \(L^2\)-subcritical case

We consider ground states of the N coupled fermionic nonlinear Schrödinger systems with the Coulomb potential V(x) in the \(L^2\) $L^2$ -subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter \(\alpha >0\) $\alpha >0$ , which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as \(\alpha \rightarrow \infty \) $\alpha \to \infty$ , where the mass concentrates at one of the singular points for the Coulomb potential V(x).