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

Abstract

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