Glasnik Matematicki, Vol. 57, No. 2 (2022), 265-280. \( \)

SOME DATKO AND BARBASHIN TYPE CHARACTERIZATIONS FOR THE UNIFORM \(h\)-INSTABILITY OF EVOLUTION FAMILIES

Tian Yue

School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, 442002 Shiyan, China
e-mail:yuet@huat.edu.cn

Abstract.   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.

2020 Mathematics Subject Classification.   34D05, 34D20

Key words and phrases.   Uniform \(h\)-instability, evolution family, growth rate, Datko type theorem, Barbashin type theorem

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https://doi.org/10.3336/gm.57.2.07

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