Abstract
In this paper, we consider the problem of exponential instability behavior of random dynamical systems described by cocycles in Banach spaces. We prove some continuous and discrete versions of Datko type theorem for the exponential instability in average of cocycles. In addition, two characterizations of the exponential instability in average in terms of Lyapunov functions are given.
Funding Statement
This work is supported by the Natural Science Foundation of Hubei Province of China (Grant Nos. 2022CFB457, 2022CFB538) and the Industry-University Cooperation Collaborative Education Project of Ministry of Education (Grant Nos. 202002137038, 202101301022).
Acknowledgments
The author is sincerely grateful to the editor and the referee for carefully reading the manuscript and for valuable suggestions which led to the improvement of this paper.
Citation
Tian Yue. "Datko type characterizations for exponential instability in average of cocycles." Hiroshima Math. J. 54 (2) 219 - 232, July 2024. https://doi.org/10.32917/h2023003
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