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-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter α>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 α→∞, where the mass concentrates at one of the singular points for the Coulomb potential V(x).