线性斜积半流非一致指数膨胀性的Datko-Pazy型定理

Datko-Pazy theorem for nonuniform exponential expansiveness of linear skew-product semiflows

主要目的是基于Lyapunov范数研究Banach空间中线性斜积半流的非一致指数膨胀性.借助Datko-Pazy方法,得到了线性斜积半流满足非一致指数膨胀的若干连续与离散形式的充要条件.所得结果推广和完善了指数稳定性与指数二分性理论中的一些已有结果 (如Datko、Pazy、Preda等).作为应用,运用所得到的主要结果研究了线性斜积半流的非一致指数二分性.

In this paper, the nonuniform exponential expansiveness of linear skew-product semiflows is studied in Banach spaces based on Lyapunov norms. Some continuous and discrete versions of necessary and sufficient conditions for nonuniform exponential expansiveness are obtained via Datko-Pazy methods.The obtained conclusions are generalizations of well-known results in exponential stability and exponential dichotomy theory(Datko, Pazy, Preda et al.). Herein, we apply the main results to the study of nonuniform exponential dichotomy of linear skew-product semiflows.