Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 126-138.

• Articles • Previous Articles     Next Articles

Generalized Homoclinic Solutions for the Stationary Extended Fisher-Kolmogorov Equation

 LI Xiao-Pei   

  1. Department of Mathematics, Zhanjiang Normal University, Guangdong Zhanjiang 524048
  • Received:2012-07-14 Revised:2013-06-25 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    广东省高等学校科技创新项目(2012KJCX0074)和湛江师范学院自然科学基金(LZL1101)资助.

Abstract:

This paper investigates the stationary extended Fisher-Kolmogorov equation

u''''-βu''+ u3-u=0,  β>0,
which has a saddle-center equilibrium u = 0 (two nonzero real and two nonzero imaginary eigenvalues). Applying a perturbation method and adjusting some phase shift constants, we prove that it has a homoclinic solution connecting a periodic solution (called generalized homoclinic solution, thereafter) near the origin for each positive constant β.

Key words: Homoclinic solutions, Periodic solutions, Reversibility

CLC Number: 

  • 37C29
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