Singular Perturbation of Nonlinear Vector Boundary Value Problem

Kang Sheng-liang; Chen Qi

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1988 > 9(9): 817-824

Kang Sheng-liang, Chen Qi. Singular Perturbation of Nonlinear Vector Boundary Value Problem[J]. Applied Mathematics and Mechanics, 1988, 9(9): 817-824.

Citation:

Kang Sheng-liang, Chen Qi. Singular Perturbation of Nonlinear Vector Boundary Value Problem[J]. Applied Mathematics and Mechanics, 1988, 9(9): 817-824.

Citation:

Kang Sheng-liang, Chen Qi. Singular Perturbation of Nonlinear Vector Boundary Value Problem[J]. Applied Mathematics and Mechanics, 1988, 9(9): 817-824.

PDF( 2531 KB)

Singular Perturbation of Nonlinear Vector Boundary Value Problem

Tongji University, Shanghai

Received Date: 1987-06-10
Publish Date: 1988-09-15

Abstract

Abstract

In this paper we study the perturbed boundary value problem of the form in which x,f β∈E^m and a₁(ε),a₂(ε),b₁(ε) and b₂(ε) are matrices of the appropriate size. Under the condition that g_y(t) is nonsingular and other suitable restrictions, the existence of the solution is proved, the asymptotic expansion of solution of order n is constructed, and the remainder term is estimated.

FullText(HTML)

References(4)

References

[1]	O'Malley,R.E.,Singular perturbation of a boundary value problem for a system of nonlinear differential equations,J.Differential Equations,8(1970),431-447.
[2]	江福汝,关于常微分方程非线性边值问题的奇异摄动,中国科学(A辑),3 (1985),232-242.
[3]	Hoppensteadt,F.,Properties of solutions of ordinary differential equations with small parameters,Comm.Pure.Appl.Math.,26(1971),807-840.
[4]	Chang,K.W.and W.A.Coppel,Singular perturbations of initial value problem over a finite interval,Arch.Rat.Mech.Anal.32(1969),268-280.