https://doi.org/10.3336/gm Glasnik matematički ISSN 0017-095X (Tisak) ISSN 1846-7989 (Online) Hrvatsko matematičko društvo i PMF-Matematički odsjek Sveučilišta u Zagrebu Bijenička cesta 30, 10000 Zagreb glasnik@math.hr http://web.math.hr/glasnik/ https://doi.org/10.3336/gm.57.2.07 Izvorni znanstveni članak Some Datko and Barbashin type characterizations for the uniform \(h\)-instability of evolution families Yue Tian yuet@huat.edu.cn 1 School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, 442002 Shiyan, China 30 12 2022 Vol 57 Svezak 2 265 280

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.

 Uniform \(h\)-instability, evolution family, growth rate, Datko type theorem, Barbashin type theorem