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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (11): 1469-1474.doi: https://doi.org/10.1007/s10483-009-1113-y

• Articles • 上一篇    

Stability of Schrödinger-Poisson type equations

黄娟 张健 陈光淦   

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China
  • 收稿日期:2008-01-02 修回日期:2009-07-10 出版日期:2009-12-02 发布日期:2009-11-01

Stability of Schrödinger-Poisson type equations

HUANG Juan, ZHANG Jian, CHEN Guang-Gan   

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China
  • Received:2008-01-02 Revised:2009-07-10 Online:2009-12-02 Published:2009-11-01

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摘要： Variational methods are used to study the nonlinear Schr¨odinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Hamiltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.

关键词: Schrödinger-Poisson type equations, ground state, existence, orbital stability

Abstract: Variational methods are used to study the nonlinear Schr¨odinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Hamiltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.

Key words: Schrödinger-Poisson type equations, ground state, existence, orbital stability

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