Singular Perturbation of Boundary Value Problem for Quasilinear Third Order Ordinary Differential Equations Involving Two Small Parameters

LIN Su-rong; TIAN Gen-bao; LIN Zong-chi

Volume 22 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(2): 199-205

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[J]. Applied Mathematics and Mechanics, 2001, 22(2): 199-205.

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Singular Perturbation of Boundary Value Problem for Quasilinear Third Order Ordinary Differential Equations Involving Two Small Parameters

1.
Mathematical Section, Fujian Broadcasting TV University, Fuzhou 350003, P. R. China;
2.
Department of Mathematics, Shanghai Railroad University, Shanghai 200333, P. R. China;
3.
Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China

Received Date: 1999-09-10
Rev Recd Date: 2000-09-10
Publish Date: 2001-02-15

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.
- two-parameters,
- singular perturbation,
- boundary value problem,
- asymptotic expansion

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References

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