Singular Perturbation of Boundary Value Problem of Systems for Quasilinear Ordinary Differential Equations

Lin Zong-chi; Lin Su-rong

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Lin Zong-chi, Lin Su-rong. Singular Perturbation of Boundary Value Problem of Systems for Quasilinear Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 1990, 11(11): 969-976.

Citation:

Lin Zong-chi, Lin Su-rong. Singular Perturbation of Boundary Value Problem of Systems for Quasilinear Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 1990, 11(11): 969-976.

Citation:

Lin Zong-chi, Lin Su-rong. Singular Perturbation of Boundary Value Problem of Systems for Quasilinear Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 1990, 11(11): 969-976.

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Singular Perturbation of Boundary Value Problem of Systems for Quasilinear Ordinary Differential Equations

Lin Zong-chi¹,
Lin Su-rong²

1.
Fujian Normal University, Fuzhou;
2.
Fujian Broadcasting TV University, Fuzhou

Received Date: 1989-11-03
Publish Date: 1990-11-15

Abstract

Abstract

In this paper, we study the singular perturbation of boundary value problem of systems for quasilinear ordinary differential equations: x′=f(t,x,y,ε),εy″=g(t,x,y,ε)y′+h(t,x,y,ε), x(0,ε)=A(ε),y(0,ε)=B(ε),y(1,ε)=C(ε) where x,f,y,h,A,B and C belong to Rⁿ and a is a diagonal matrix.Under the appropriate assumptions, using the technique of diagonalization and the theory of differential inequalities we obtain the existence of solution and its componentwise uniformly valid asymptotic estimation.
- quasilinear systems,
- singularly perturbed boundary value problem,
- diagonalization and differential inequality,
- asymptotic expansion

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References(7)

References

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