The ground states for Hartree–Fock systems with a general nonlinearity

We consider the least energy solutions of Hatree–Fock system with the coupling term ϕu,v$$ {\phi}_{u,v} $$ in the two equations, and the nonlinearity are general subcritical with a small perturbation. By Nehari's manifold approach, the existence of nontrivial ground state solutions is obtained. The asymptotic behaviors with respect to parameters λ$$ \lambda $$ and β$$ \beta $$ are also studied.