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

YUE Tian; SONG Xiaoqiu

doi:10.3969/j.issn.1000-5641.201911042

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Nov. 2020

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YUE Tian, SONG Xiaoqiu. Datko-Pazy theorem for nonuniform exponential expansiveness of linear skew-product semiflows[J]. Journal of East China Normal University (Natural Sciences), 2020, (6): 30-37. doi: 10.3969/j.issn.1000-5641.201911042

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YUE Tian, SONG Xiaoqiu. Datko-Pazy theorem for nonuniform exponential expansiveness of linear skew-product semiflows[J]. Journal of East China Normal University (Natural Sciences), 2020, (6): 30-37. doi: 10.3969/j.issn.1000-5641.201911042

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

doi: 10.3969/j.issn.1000-5641.201911042

YUE Tian^1
,,
SONG Xiaoqiu²

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
Publish Date: 2020-11-25

Abstract

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.
- linear skew-product semiflows,
- nonuniform exponential expansiveness,
- nonuniform exponential dichotomy,
- Datko-Pazy theorem

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References(12)

References

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