The nonlinear Schrödinger equations with combined nonlinearities of power-type and Hartree

Abstract

This paper is devoted to a comprehensive study of the nonlinear Schrödinger 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.