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Research Article | Open Access

Barbashin type characterizations for nonuniform h-dichotomy of evolution families

School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, Shiyan 442002, China
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Abstract

The aim of this paper is to give some Barbashin type characterizations for the nonuniform h-dichotomy of reversible evolution families in Banach spaces. Two necessary and sufficient conditions for the nonuniform h-dichotomy are pointed out using some important sets of growth functions. Additionally, as particular cases, we obtain a Barbashin type characterization for nonuniform exponential dichotomy and a necessary and sufficient condition for the nonuniform polynomial dichotomy.

Keywords

nonuniform h-dichotomyevolution familygrowth rateBarbashin type theoremnonuniform exponential dichotomynonuniform polynomial dichotomy
CLC number: 34D05, 34D09

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 26357-26371
DOI: 10.3934/math.20231345

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Cite this article:
Yue T. Barbashin type characterizations for nonuniform h-dichotomy of evolution families. AIMS Mathematics, 2023, 8(11): 26357-26371. https://doi.org/10.3934/math.20231345

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Received: 10 July 2023
Revised: 04 September 2023
Accepted: 05 September 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)