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

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

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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. 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

Abstract

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

2010 MSC Number:

O175.3

LIN Su-rong;TIAN Gen-bao;LIN Zong-chi. SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS. Applied Mathematics and Mechanics (English Edition), 2001, 22(2): 229-236.

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

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