Acta Mathematicae Applicatae Sinica

, Volume 13, Issue 4, pp 414–424 | Cite as

Existence and uniqueness of global solutions of onR2

  • Jiu Quansen 
  • Liu Jun 
Article

Abstract

In this paper, we consider the solutions of the nonlinear Schrödinger equations ∂u/∂tiΔu+|u| p u=f andu(x,0)=u0(x), whereu is defined onR+×R2. We prove the existence and uniqueness of global weak solutions of the above equations. Lastly, we consider the special case:p=2, and we obtain the strong solutions.

Key words

Nonlinear Schrödinger equations iteration 

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Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1997

Authors and Affiliations

  • Jiu Quansen 
    • 1
  • Liu Jun 
    • 2
  1. 1.Department of MathematicsCapital Normal UniversityBeijingChina
  2. 2.Institute of Applied Mathematicsthe Chinese Academy of SciencflesBeijingChina

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