演化家族统一\(h\) -不稳定性的一些Datko和Barbashin型表征

Pub Date : 2022-12-30 DOI:10.3336/gm.57.2.07

Tian Yue

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引用次数: 1

摘要

利用一些重要的增长率集，给出了演化族在Banach空间中一致\(h\) -不稳定性的Datko和Barbashin型表征。我们证明了均匀\(h\) -不稳定性的四个Datko型表征定理和两个Barbashin型表征定理。得到了稳定性理论中一些著名结果(Barbashin (1967)， Datko(1972))的均匀\(h\) -不稳定性的变体。

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Some Datko and Barbashin type characterizations for the uniform \(h\)-instability of evolution families

The aim of this paper is to give some Datko and Barbashin type characterizations for the uniform \(h\)-instability of evolution families in Banach spaces, by using some important sets of growth rates. We prove four characterization theorems of Datko type and two characterization theorems of Barbashin type for uniform \(h\)-instability. Variants for uniform \(h\)-instability of some well-known results in stability theory (Barbashin (1967), Datko (1972)) are obtained.

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