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

Abstract

The primary goal of this paper is to present a comprehensive study of the nonlinear Schrödinger equations with combined nonlinearities of the power-type and Hartree-type. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schrödinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.

Keywords

Global well-posedness / Scattering / blowup / Morawetz estimates / Perturbation principles

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