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Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (2): 229-236.

• 论文 • 上一篇    下一篇

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

林苏榕1, 田根宝2, 林宗池3   

  1. 1. Mathematical Section, Fujian Broadcasting TV University, Fuzhou 350003, P. R. China;
    2. Department of Mathematics, Shanghai Railroad University, Shanghai00333, P. R. China;
    3. Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China
  • 收稿日期:1999-09-10 修回日期:2000-09-10 出版日期:2001-02-18 发布日期:2001-02-18

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

LIN Su-rong1, TIAN Gen-bao2, LIN Zong-chi3   

  1. 1. Mathematical Section, Fujian Broadcasting TV University, Fuzhou 350003, P. R. China;
    2. Department of Mathematics, Shanghai Railroad University, Shanghai00333, P. R. China;
    3. Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China
  • Received:1999-09-10 Revised:2000-09-10 Online:2001-02-18 Published:2001-02-18

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摘要： The singularly perturbed boundary value problem for quasilinear third-order ordinary differential equation involving two small parameters has been considered. For the three cases ε/μ2→0(μ→0), μ2/ε→0(ε→0) and ε=μ2, the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.

关键词: two-parameters, singular perturbation, boundary value problem, asymptotic expansion

Abstract: The singularly perturbed boundary value problem for quasilinear third-order ordinary differential equation involving two small parameters has been considered. For the three cases ε/μ2→0(μ→0), μ2/ε→0(ε→0) and ε=μ2, the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.

Key words: two-parameters, singular perturbation, boundary value problem, asymptotic expansion

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