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 


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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  1. [1]
    J.L. Lions. Quelques Méthodes de Résolution des Problèm aux Limites Nonlinéaires. DONOD, GAUTHIER-VILLARS, Paris 1969.Google Scholar
  2. [2]
    Ding Xiaxi, Luo Peizhu and Li Yanyan. The Solvability of Nonlinear Parabolic Equation in Ba Space.J. of Central Teachers College (Natural Science Edition), 1985, 2: 1–9.Google Scholar
  3. [3]
    Li Congming. Global Properties of The Solutions of Nonlinear Schrödinger Equations on a Bounded Domain.J. Sys. Sci. & Math. Scis., 1984, 4(2): 160–164.Google Scholar
  4. [4]
    Li Daqian. Nonlinear Evolutional Equations. Science Press, Beijing, 1989.Google Scholar
  5. [5]
    Yao Jingqi. Time Decay of Solutions to a Nonlinear Schrödinger Equation in an Exterior Domain inR 2.Nonlinear Analysis, 1992, 19: 563–571.Google Scholar
  6. [6]
    M. Tsutsumi. On Smooth Solutions to the Initial-boundary Value Problem for the Nonlinear Schrödin -ger Equation in Two Space Dimensions.Nonlinear Analysis, 1989, 13: 1051–1056.Google Scholar
  7. [7]
    L. Segal. Nonlinear Semi-groups.Ann. Math., 1963, 78: 339–364.Google Scholar
  8. [8]
    H. Brézis and T. Gallouet. Nonlinear Schrödinger Evolution Equations.Nonlinear Analysis, 1980, 4: 677–681.Google Scholar
  9. [9]
    Yao Jingqi. The Solutions of One Type of Nonlinear Schrödinger Equations.Chinese Annals of Mathematics, 1986, 7A(4): 413–422 (in Chinese).Google Scholar
  10. [10]
    R. Temam. Navier-Stokes Equations. Elasevier Science Publishers B.V., Netherlands, 1985.Google Scholar

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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