具有广义指数型二分性的扰动系统的周期解

Periodic solution of perturbed system with generalized exponential dichotomy

经典的指数型二分性理论已经得到较为完善的发展,但经典指数型二分性相对较强,限制了很多动力学行为.为了得到更多的动力学性质,在现有广义指数型二分性概念的基础上,主要采用压缩不动点定理,探讨了当线性部分具有广义指数型二分性时,扰动系统周期解的存在唯一性.得到了该系统周期解存在且唯一的一些充分条件.

The classical exponential dichotomy had been well developed, while the concept of classical expo-nential dichotomy was always too strong.It restricted many dynamic behavior.A set of sufficient conditions were obtained for the periodic solutions of non-autonomous nonlinear system if the linear part admited a gener-alized exponential dichotomy.