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一类二阶微分差分方程边值问题的奇摄动解

徐钧涛

徐钧涛. 一类二阶微分差分方程边值问题的奇摄动解[J]. 应用数学和力学, 1988, 9(7): 629-640.
引用本文: 徐钧涛. 一类二阶微分差分方程边值问题的奇摄动解[J]. 应用数学和力学, 1988, 9(7): 629-640.
Xu Jun-tao. Singular Perturbation Solution of Boundary-Value Problem for a Second-Order Differential-Difference Equation[J]. Applied Mathematics and Mechanics, 1988, 9(7): 629-640.
Citation: Xu Jun-tao. Singular Perturbation Solution of Boundary-Value Problem for a Second-Order Differential-Difference Equation[J]. Applied Mathematics and Mechanics, 1988, 9(7): 629-640.

一类二阶微分差分方程边值问题的奇摄动解

Singular Perturbation Solution of Boundary-Value Problem for a Second-Order Differential-Difference Equation

  • 摘要: 本文利用两变量展开直接构造边界层项的方法,讨论了一类二阶微分差分方程边值问题的奇摄动解,构造了形式渐近解,作出了余项估计,从而证明了解的存在性.
  • [1] Lange, C.G. and R.M. Miura, Singular perturbation analysis of boundary value problem for differential-difference equation, SIMA J. Appl. Math., 42,3 (1982), 502-531.
    [2] Nayfeh, A.H., Perturbation methods. Ist ed. New York, John Wiley and Sons (1973).
    [3] 江福汝,关于边界层方法,应用数学和力学,2, 5 (1981), 461-474.
    [4] 江福汝,关于椭圆型方程的奇摄动,复旦大学学报(自然科学版),2(1978),29-37.
    [5] Murray, H.P. and F.W. Hams. Maximum Principles in Differential Equation, Prentice-Hall, Englewood Cliffs, New Jersey, (1967).
    [6] Chang, K.W. and F.A. Howes, Nonlinear Singular Perturbation Phenomena: Theory and Application, lst ed. New York, Springer-Verlag (1984).
    [7] O'Malley, R.E., Introduction to Singular Perturbations. lst ed., New York, Academic Press (1974).
    [8] Xu Jun-tao. Singular perturbation of boundary-value problem for a second-order differentialdiference equation. Ann. of Diff. Eqs., 2, 1 (1986), 47-64.
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出版历程
  • 收稿日期:  1987-04-20
  • 刊出日期:  1988-07-15

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