摘要
用 Hadamar和 Bogoliubov的方法,在常微分方程、泛函微分方程以及半线性抛物型方程所能满足的条件下对Banach或Hilbert空间上的非自治抽象微分方程建立了不变流形理论。首先,对相应的线性方程提出了“广义指数二分性”概念并讨论了它和线性方程谱的关系,然后,我们给出了不变流形存在性结论以及强稳定(不稳定)流形、弱稳定(不稳定)流形和弱双曲流形的分类。进而,我们对这些不变流形给出了C^k光滑性、周期性、概周期性和吸斥性的结论。
In this paper mainly using Hadamard and Bogoliubov's method the theory of invariant manifolds for abstract nonautonomous differential equations in Ba-nach or Hilbert spaces under conditions satisfied by O.D.E., F.D.E. and semili-near parabolic equations is set up. First, we put forward the concept of “generalized exponential dichotomy” of the corresponding linear equations and discuss the relations between it and the spectrums of these linear equations. Next,the existence of invariant manifolds and a classification: strong stable (unstable) manifolds, weak stable (unstable) manifolds and weak hyperbolic manifolds are obtained. Furthermore, results about Ck-smoothness, periodicity, almost-periodicity, attractivity and repellency of these invariant manifolds are given.
出处
《数学进展》
CSCD
北大核心
1993年第1期1-45,共45页
Advances in Mathematics（China）
关键词
广义
指数二分性
微分方程
generalized exponential dichotomy
dynamical systems of infinite dimension
strong stable (unstable) manifolds
weak stable (unstable) manifolds
weak hyperbolic manifolds
Ck-smoothness
periodicity
almost-periodicity
attractivity
repellenc
