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| 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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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.
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Received: 08 May 2017
Published: 12 September 2018
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Cite this article:
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.
URL:
https://www.zjujournals.com/sci/EN/Y2018/V45/I5/545
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线性斜积半流的一致指数稳定性的若干刻画
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
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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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