无穷区域上非线性向量方程初值问题的解的渐近性质

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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∈E^m,y,g∈Eⁿ,实的小参数ε>0,0≤t<+∞,在g_r(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{S_R(ε)}∈E^m+n,使得如果(ξ(ε),η(ε))∈S_R(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。

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.

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