Multiple positive solutions for a coupled nonlinear Hartree type equations with perturbations

In this paper we study the existence of multiple nontrivial solutions of coupled nonlinear Hartree equations with perturbations. This type of equations was used to describe the multi-component Bose-Einstein condensates and the basic quantum chemistry model of small number of electrons interacting with static nuclei. By combining the Nehari constraint and minimax methods, we prove the existence of two nontrivial solutions of the equations.