巴拿赫空间中演化过程非一致指数二分性的Datko-Pazy型定理  

Datko-Pazy theorem for the nonuniform exponential dichotomy of evolutionary process in Banach spaces

作　　者：岳田 宋晓秋[3] YUE Tian;SONG Xiaoqiu(School of Science,Hubei University of Automotive Technology,Shiyan 442002,Hubei Province,China;Key Laboratory of Automotive Power Train and Electronics(Hubei University of Automotive Technology),Shiyan 442002,Hubei Province,China;School of Mathematics,China University of Mining and Technology,Xuzhou 221116,Jiangsu Province,China)

机构地区：[1]湖北汽车工业学院理学院,湖北十堰442002 [2]汽车动力传动与电子控制湖北省重点实验室(湖北汽车工业学院),湖北十堰442002 [3]中国矿业大学数学学院,江苏徐州221116

出　　处：《浙江大学学报（理学版）》2021年第1期41-45,56,共6页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11502075);汽车动力传动与电子控制湖北省重点实验室开放项目(ZDK1202004).

摘　　要：基于Lyapunov范数研究了巴拿赫空间中演化过程的非一致指数二分性,借助Datko-Pazy方法,得到了演化过程满足非一致指数二分性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的部分已有结果。The nonuniform exponential dichotomy of evolutionary process in Banach spaces is studied based on the Lyapunov norms.Some continuous and discrete versions of necessary and sufficient conditions for nonuniform exponential dichotomy are obtained by applying Datko-Pazy methods.The obtained conclusions are generalizations of the well-known results in exponential stability and exponential dichotomy theory.

关 键 词：演化过程 非一致指数二分性 Datko-Pazy型定理 

分 类 号：O175.13[理学—基础数学]