数学物理学报(英文版) ›› 1989, Vol. 9 ›› Issue (4): 373-383.

• 论文 • 上一篇    下一篇

EXISTENCE OF GENERALIZED SOLUTION AND ORBITAL STABILITY OF STANDING WAVES FOR NONLINEAR SINGULAR SCHRÖDINGER EQUATION

张波   

  1. Inst. of Sys. Sci., Academia Sinica, Beijing, China
  • 收稿日期:1987-11-18 出版日期:1989-12-25 发布日期:1989-12-25

EXISTENCE OF GENERALIZED SOLUTION AND ORBITAL STABILITY OF STANDING WAVES FOR NONLINEAR SINGULAR SCHRÖDINGER EQUATION

Zhang Bo   

  1. Inst. of Sys. Sci., Academia Sinica, Beijing, China
  • Received:1987-11-18 Online:1989-12-25 Published:1989-12-25

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摘要： The existence of generalized solution to the initial value problem iut+△u+k/(xN)uXN+q(x)u+|u|p-1u=0 on RN is studied, By Galerkin method, we prove that the solution always exists for every initial value in H1(RN; k) if 1 < p < (N+k)/(N+k-2), N ≥ 2. Finally, we prove orbital stability of standing waves for nonlinear singular Schrödinger equation.

Abstract: The existence of generalized solution to the initial value problem iut+△u+k/(xN)uXN+q(x)u+|u|p-1u=0 on RN is studied, By Galerkin method, we prove that the solution always exists for every initial value in H1(RN; k) if 1 < p < (N+k)/(N+k-2), N ≥ 2. Finally, we prove orbital stability of standing waves for nonlinear singular Schrödinger equation.

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