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Glasnik matematički, Vol. 57 No. 2, 2022.

Izvorni znanstveni članak

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

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

Tian Yue orcid id orcid.org/0000-0003-2811-9444 ; School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, 442002 Shiyan, China

Puni tekst: engleski pdf 151 Kb

str. 265-280

preuzimanja: 147

citiraj

Preuzmi JATS datoteku

Sažetak

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.

Ključne riječi

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

Hrčak ID:

289608

URI

https://hrcak.srce.hr/289608

Datum izdavanja:

30.12.2022.

Posjeta: 345 *

Publication date: 30 December 2022

Volume: Vol 57

Issue: Svezak 2

Pages: 265-280

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

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

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

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

Tian Yue[1]

Email: yuet@huat.edu.cn

 

[1] School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, 442002 Shiyan, China

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.

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