华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (1): 37-42.

• 应用数学与基础数学 • 上一篇    下一篇

非线性奇摄动方程的脉冲解

朱振波1,2, 林武忠1,2   

  1. 1.华东师范大学 数学系,上海 200062; 2.上海高校计算科学E-研究院 上海交通大学研究所,上海 200030
  • 收稿日期:2008-03-21 修回日期:2008-06-25 出版日期:2009-01-25 发布日期:2009-01-25
  • 通讯作者: 林武忠

Spike-like solutions of nonlinear singularly perturbed equations (Chinese)

ZHU Zhen-bo1,2, LIN Wu-zhong1,2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China; 2.Division of Computational Science, E-institute of Shanghai Universities SJTU, Shanghai 200030,China
  • Received:2008-03-21 Revised:2008-06-25 Online:2009-01-25 Published:2009-01-25
  • Contact: LIN Wu-zhong

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摘要： 对一类比较一般的施图姆-刘维尔型奇摄动问题,~%
揭示了其脉冲解的存在性,~并相应地给出了脉冲解的存在性条件.~%
利用边界层函数法构造其一致有效渐近解,~以及进行余项估计.~%
最后通过一个例子来进一步验证前面的结论.

关键词: 奇摄动, 边界层函数, 脉冲解, 奇摄动, 边界层函数, 脉冲解

Abstract: The existence of spike-like solutions of a class of
Sturm-Liouville singularly perturbed problem was investigated and
its sufficient condition was given. Meanwhile, the uniformly valid
asymptotic solutions were constructed by the method of boundary
layer functions and remainder estimation was presented. Finally, an
example was given to illustrate the obtained results.

Key words: boundary layer functions, spike-like solutions, singular perturbation, boundary layer functions, spike-like solutions

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