The nonlinear Schr\"odinger equations with combined nonlinearities of   power-type and Hartree
  This paper is devoted to a comprehensive study of the nonlinear Schr\"odinger equations with combined nonlinearities of the power-type and Hartree-type in any dimension n\ge3. With some structural conditions, a nearly whole picture of the interactions of these nonlinearities in the energy space is given. The method is based on the Morawetz estimates and perturbation principles. 
Daoyuan Fang and Zheng Han