Existence and multiplicity of nontrivial solutions of weakly coupled nonlinear Hartree type elliptic system

In the present paper, we are concerned with the existence of bound and ground states solutions of coupled nonlinear Hartree type system with nonlocal interaction. This type equations arises from the basic quantum chemistry model of small number of electrons interacting with static nucleii. First, we prove the existence bound and ground states solutions for two coupled nonlinear Hartree type system. Second, we find some new conditions to guarantee the existence of positive ground state solutions for general nonlinear coupled Hartree type system. These conditions are better than previous work of Wang and Shi (Calc Var Partial Differ Equ 56:168, 2017) even for two coupled system. Finally, some properties of the solutions are also obtained.