华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (6): 30-37.doi: 10.3969/j.issn.1000-5641.201911042

• 数学 • 上一篇    下一篇

线性斜积半流非一致指数膨胀性的Datko-Pazy型定理

岳田1, 宋晓秋2   

  1. 1. 湖北汽车工业学院 理学院, 湖北 十堰 442002;
    2. 中国矿业大学 数学学院, 江苏 徐州 221116
  • 收稿日期:2019-10-12 发布日期:2020-12-01
  • 作者简介:岳 田, 男, 讲师, 研究方向为微分系统定性理论. E-mail: yuetian@cumt.edu.cn
  • 基金资助:
    国家自然科学基金(11502075); 湖北汽车工业学院教学研究与改革项目(JY2019016)

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

YUE Tian1, SONG Xiaoqiu2   

  1. 1. School of Sciences, Hubei University of Automotive Technology, Shiyan Hubei 442002, China;
    2. School of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221116, China
  • Received:2019-10-12 Published:2020-12-01

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摘要： 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.

关键词: 线性斜积半流, 非一致指数膨胀性, 非一致指数二分性, Datko-Pazy型定理

Abstract: 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.

Key words: linear skew-product semiflows, nonuniform exponential expansiveness, nonuniform exponential dichotomy, Datko-Pazy theorem

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