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浙江大学学报（理学版）
浙江大学学报（理学版）  2018, Vol. 45 Issue (5): 545-548    DOI: 10.3785/j.issn.1008-9497.2018.05.005
数学与计算机科学     
线性斜积半流的一致指数稳定性的若干刻画
岳田1, 宋晓秋2
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
Some characterizations for the uniform exponential stability of linear skew-product semiflows
YUE Tian1, SONG Xiaoqiu2
1. School of Science, Hubei University of Automotive Technology, Shiyan 442002, Hubei Province, China;
2. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu Province, China
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摘要： 基于线性斜积半流的定义，引入了Banach空间中该类动力系统一致指数稳定的概念.借助稳定性理论中的Datko型方法，讨论了斜积半流一致指数稳定的特征，建立了其一致指数稳定的若干充要条件.所得结论推广了指数稳定性及指数不稳定性中一些已有的经典结论（如DATKO、ROLEWICZ、MEGAN、BUSE等）.
关键词： 线性斜积半流;  一致指数稳定性;  巴拿赫空间    
Abstract: Based on the definition of linear skew-product semiflows, a uniform exponential stability concept of dynamical systems is presented in Banach spaces. The main purpose of this paper is to give several characterizations for the uniform exponential stability of linear skew-product semiflows by means of Datko's approach in stability theory. Some necessary and sufficient conditions concerning the uniform exponential stability of linear skew-product semiflows are given. The obtained conclusions are generalizations of the well-known results about the exponential stability and exponential instability.
Key words: linear skew-product semiflow    uniform exponential stability    Banach space
收稿日期: 2017-05-08 出版日期: 2018-09-12
CLC:  O175.13  
基金资助: 湖北省教育厅科学技术研究项目（B2018067）.
作者简介: 岳田(1988-),ORCID:http://orcid.org/0000-0002-3371-5673,男,硕士,讲师,主要从事微分系统的渐近行为研究,E-mail:yuetian@cumt.edu.cn.
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引用本文:

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.

YUE Tian, SONG Xiaoqiu. Some characterizations for the uniform exponential stability of linear skew-product semiflows. Journal of Zhejiang University (Science Edition), 2018, 45(5): 545-548.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.05.005    或    https://www.zjujournals.com/sci/CN/Y2018/V45/I5/545

[1] DATKO R. Uniform asymptotic stability of evolutionary processes in a Banach space[J]. SIAM J Math Anal, 1973, 3(3):428-445.
[2] ROLEWICZ S. On uniform N-equistability[J]. J Math Anal Appl, 1986, 115(2):434-441.
[3] MEGAN M,SASU A L, SASU B. Perron conditions for uniform exponential expansiveness of linear skew-product flows[J]. Monatsh Math, 2003, 138(2):145-157.
[4] MEGAN M,SASU A L, SASU B. Exponential stability and exponential instability for linear skew-product flows[J]. Math Bohem, 2004, 129(3):225-243.
[5] MEGAN M,SASU A L, SASU B. Exponential instability of linear skew-product semiflows in terms of Banach function spaces[J]. Results Math, 2004, 45(3):309-318.
[6] MEGAN M, BULIGA L. Functionals on normed function spaces and exponential instability of linear skew-product semiflows[J]. Bull Belg Math Soc Simon Stevin, 2007, 14(2):355-362.
[7] 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.
[8] BUSE C, NICULESCU C P. An ergodic characterization of uniformly exponentially stable evolution families[J]. Bull Math Soc Sci Math Moumanie, 2009, 52(1):33-40.
[9] LUPA N, MEGAN M, POPA I L. On weak exponential stability of evolution operators in Banach spaces[J]. Nolinear Anal, 2010, 73(8):2445-2450.
[10] STOICA C, MEGAN M. On uniform exponential stability for skew-evolution semiflows on Banach spaces[J]. Nolinear Anal, 2010, 72(3/4):1305-1313.
[11] HAI P V. Continuous and discrete characterizations for the uniform exponential stability of linear skew-evolution semiflows[J]. Nolinear Anal, 2010, 72(12):4390-4396.
[12] YUE T, SONG X Q, LI D Q. On weak exponential expansiveness of skew-evolution semiflows in Banach spaces[J]. J Inequal Appl, 2014, 2014:165.
[13] 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. YUE T, LEI G L, SONG X Q. Some characterizations for the uniform exponential expansiveness of linear skew-evolution semiflows[J]. Advances in Mathematics, 2016, 45(3):433-442.
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