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无穷区域上非线性向量方程初值问题的解的渐近性质

康盛亮 张安江

康盛亮, 张安江. 无穷区域上非线性向量方程初值问题的解的渐近性质[J]. 应用数学和力学, 1987, 8(8): 669-688.
引用本文: 康盛亮, 张安江. 无穷区域上非线性向量方程初值问题的解的渐近性质[J]. 应用数学和力学, 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.

无穷区域上非线性向量方程初值问题的解的渐近性质

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

  • 摘要: 本文研究无穷域上的初值问题:其中x,f∈Em,y,g∈En,实的小参数ε>0,0≤t<+∞,在gr(t)是非奇异的和其它适当的假设下,证明了存在一系列k+m*维流形{SR(ε)}∈Em+n,使得如果(ξ(ε),η(ε))∈SR(ε),方程(1.1)是正则退化的,并作出了解的R阶渐近展开式及其余项估计。
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    [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.
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出版历程
  • 收稿日期:  1986-06-06
  • 刊出日期:  1987-08-15

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