Applied Mathematics and Mechanics

, Volume 21, Issue 3, pp 265–274 | Cite as

A note on bifurcations ofu+μ(u−uk)=0(4≤kεZ+)

  • Li Changpin


Bifurcations of one kind of reaction-diffusion equations,u+μ(u−uk)=0(μ is a parameter, 4≤kεZ+), with boundary value condition u(0)=u(π)=0 are discussed. By means of singularity theory based on the method of Liapunov-Schmidt reduction, satisfactory results can be acquired.

Key words

Liapunov-Schmidt reduction singularity theory bifurcation 

CLC number



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  1. [1]
    Fife P C.Mathematical Aspects of Reaction and Diffusing Systems[M].Lecture Notes in Biomathematics, Vol 28. Berlin/Heidelberg/New York: Springer-Verlag, 1979.Google Scholar
  2. [2]
    Ye Qixao, Li Zhengyuan.Introduction to Reaction-Diffusion Equations[M]. Beijing: Science Press, 1994. (in Chinese)Google Scholar
  3. [3]
    Chow S N, Hale J K.Methods of Bifurcation Theory[M]. New York: Springer-Verlag, 1982.Google Scholar
  4. [4]
    Golubitsky M, Schaeffer D G.Singularities and Groups in Bifurcation Theory[M]. Vol. 1, New York: Springer-Verlag, 1985.Google Scholar
  5. [5]
    Lu Qishao.Bifurcation and Singularity[M]. Shanghai: Shanghai Scientific and Technological Education Publishing House, 1995. (in Chinese)Google Scholar
  6. [6]
    Tang Yun.Foundation of Symmetry Bifurcation Theory[M]. Beijing: Science Press, 1998. (in Chinese)Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2000

Authors and Affiliations

  • Li Changpin
    • 1
  1. 1.Department of MathematicsShanghai UniversityShanghaiP R China

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