华东师范大学学报（自然科学版） >

2020 , Vol. 2020 >Issue 6: 30 - 37

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911042

数学

线性斜积半流非一致指数膨胀性的Datko-Pazy型定理

  • 岳田 ,
  • 宋晓秋
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  • 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
岳 田, 男, 讲师, 研究方向为微分系统定性理论. E-mail: yuetian@cumt.edu.cn

收稿日期: 2019-10-12

  网络出版日期: 2020-12-01

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)

收起

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

  • YUE Tian ,
  • SONG Xiaoqiu
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  • 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 date: 2019-10-12

  Online 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

本文引用格式

岳田 , 宋晓秋 . 线性斜积半流非一致指数膨胀性的Datko-Pazy型定理[J]. 华东师范大学学报（自然科学版）, 2020 , 2020(6) : 30 -37 . DOI: 10.3969/j.issn.1000-5641.201911042

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

参考文献

[1] DATKO R. Extending a theorem of A. M. Liapunov to Hilbert spaces [J]. J Math Anal Appl, 1970, 32(3): 610-616
[2] DATKO R. Uniform asymptotic stability of evolutionary processes in Banach space [J]. SIAM J Math Anal, 1972, 3(3): 428-445
[3] PAZY A. On the applicability of Lyapunov’s theorem in Hilbert space [J]. SIAM J Math Anal, 1972, 3(2): 291-294
[4] 岳田, 雷国梁, 宋晓秋. 线性斜演化半流一致指数膨胀性的若干刻画 [J]. 数学进展, 2016, 45(3): 433-442
[5] 岳田, 宋晓秋. Banach空间中GC(0, e) 类广义发展算子的一致指数不稳定性 [J]. 中山大学学报(自然科学版), 2018, 57(5): 150-154
[6] MUREŞAN M, PREDA C, PREDA P. Individual stability and instability for evolutionary processes [J]. Acta Math Hungar, 2017, 153(1): 16-23
[7] BARREIRA L, VALLS C. Admissibility for nonuniform exponential contractions [J]. J Differ Equ, 2010, 249(11): 2889-2904
[8] PREDA P, PREDA C, MORARIU C. Exponential stability concepts for evolution families on \scriptsize $ {\mathbb{R}} $ \normalsize [J]. Monatsh Math, 2015, 178(4): 611-631
[9] 岳田, 宋晓秋. 线性斜积半流的一致指数稳定性的若干刻画 [J]. 浙江大学学报(理学版), 2018, 45(5): 545-548
[10] BǍTǍRAN F, PREDA C, PREDA P. Extending some results of L. Barreira and C. Valls to the case of linear skew-product semiflows [J]. Results Math, 2017, 72(1): 965-978
[11] PREDA C, PREDA P, BǍTǍRAN F. An extension of a theorem of R. Datko to the case of (non)uniform exponential stability of linear skew-product semiflows [J]. J Math Anal Appl, 2015, 425(2): 1148-1154
[12] PREDA C, ONOFREI O R. Nonuniform exponential dichotomy for linear skew-product semiflows over semiflows [J]. Semigroup Forum, 2018, 96(2): 241-252
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