Sharp criteria for the nonlinear Schrödinger equation with combined nonlinearities of power-type and Hartree-type

Abstract

This paper deals with the Cauchy problem of the nonlinear Schrödinger equation with Combined Nonlinearities. By using the generalized Gagliardo–Nirenberg inequalities, when and for all , we obtain a sharp threshold for global existence and blow-up of solutions.

Keywords:

• Nonlinear Schrödinger equation
• Hartree-type
• sharp criteria
• blow-up solution
• global existence

AMS Subject Classifications:

• 35Q55
• 35B44

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Fund of Lab of Security Insurance of Cyberspace, Sichuan Province P.R. China [grant number szjj2014-080]; Scientific Research Fund of Sichuan Provincial Education Department of China [grant number 15ZA0135].