Journal of East China Normal University(Natural Science) ›› 2020, Vol. 2020 ›› Issue (6): 30-37.doi: 10.3969/j.issn.1000-5641.201911042

• Mathematics • Previous Articles     Next Articles

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

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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