Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval

Kang Sheng-liang; Zhang An-jiang

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1987 > 8(8): 669-688

Kang Sheng-liang, Zhang An-jiang. Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval[J]. Applied Mathematics and Mechanics, 1987, 8(8): 669-688.

Citation:

Kang Sheng-liang, Zhang An-jiang. Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval[J]. Applied Mathematics and Mechanics, 1987, 8(8): 669-688.

Citation:

Kang Sheng-liang, Zhang An-jiang. Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval[J]. Applied Mathematics and Mechanics, 1987, 8(8): 669-688.

PDF( 1101 KB)

Asymptotic Properties of Solutions of Nonlinear Vector Initial Value Problem on the Infinite Interval

Tongji University, Shanghai

Received Date: 1986-06-06
Publish Date: 1987-08-15

Abstract

Abstract

In this paper we study initial value problems on the infinite interval: where x, f∈E^m, y, g∈Eⁿ,εare real small positive parameters,0≤t<+∞. On condition that g_y(t) is nonsingular and under other assumptions, we have proved that there areserial (k+m*)-dimensionalmanifolds {S_R(ε)}∈E^m+n such that (1.1) degenerates regularly provided(ξ(ε),η(ε))∈S_R(ε). Besides, the R-order asymptotic expansions of solutions are constructed, and their errors are estimated.

FullText(HTML)

References(9)

References

[1]	Тихонов А.Н.,Снстемы днфференпиалъных уравнений,содержащие малые параметры при производных,Маmeмаmuческuu,73,31(1952),575-586.
[2]	Levin,J.J.and N.Levinson,Singular perturbations of nonlinear systems of differential equations and associated boundary layer equation,J.Rational Mech.Anal.,3(1954),247-270.
[3]	Hoppensteadt,F.Singular perturbations on the infinite interval,Trans.Amer.Math.Soc.,123,2(1966),521-535.
[4]	Hoppensteadt,F.,Stability in systems with parameters,J.math.Anal.Appl.18,1(1987).129-134.
[5]	Levin,J.J.,Singular perturbations of nonlinear systems of differential equations related to conditional stability,Duke.J Math.,23,4(1956).609-620.
[6]	Flatto,L.and N.Levinson,Periodic solutions of singular perturbed systems,J.Rational Mech.Anal.,4(1955),943-950.
[7]	Hoppensteadt,F.,Properties of solutions of ordinary differential equations with small parameter,Comm.Pure.Appl.Math:24(1971),807-840.
[8]	Coppel,W.A.,Dichotomies and reducibility,J.Diff.Equations 3(1967),500-521.
[9]	Chang,K.W.and W.A.Coppel,Singular perturbations of initial value problems over a finite interval,Arch.Rational Meth.Anal.,32,4(1969),268-280．