线性斜积半流非一致指数渐近行为的若干刻画
Some Characterizations of Nonuniform Exponential Asymptotic Behaviors for Linear Skew-Product Semi?ows
DOI: 10.12677/AAM.2023.126263, PDF,    科研立项经费支持
作者: 汪 婷*, 刘紫依, 岳 田：湖北汽车工业学院数理与光电工程学院，湖北 十堰
关键词: 线性斜积半流；稳定性；膨胀性；Linear Skew-Product Semi?ows； Stability； Expansiveness
摘要: 本文主要研究Banach空间上线性斜积半流非一致指数渐近行为的Datko型特征以及平均型特征。借助Lyapunov范数技术得到了线性斜积半流满足非一致指数稳定与膨胀的若干充要条件。所得结果推广了微分系统稳定性理论中一些已有结果。
Abstract: The aim of this paper is to study the Datko’s characterization for the nonuniform exponential stabil-ity and the nonuniform exponential expansiveness of linear skew-product semiflows in Banach spaces, respectively. The necessary and sufficient conditions for the nonuniform exponential as-ymptotic behaviors are obtained via Lyapunov norms. The obtained conclusions are generalizations of the well-known results in stability theory.
文章引用：汪婷, 刘紫依, 岳田. 线性斜积半流非一致指数渐近行为的若干刻画[J]. 应用数学进展, 2023, 12(6): 2623-2629. https://doi.org/10.12677/AAM.2023.126263

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