Barbashin type characterizations for nonuniform <i>h</i>-dichotomy of evolution families

Tian Yue; Tian Yue

doi:10.3934/math.20231345

AIMS Mathematics

2023, Volume 8, Issue 11: 26357-26371. doi: 10.3934/math.20231345

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Research article

Barbashin type characterizations for nonuniform h-dichotomy of evolution families

Tian Yue ^,

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

Received: 10 July 2023 Revised: 04 September 2023 Accepted: 05 September 2023 Published: 14 September 2023
MSC : 34D05, 34D09

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.
- nonuniform h-dichotomy,
- evolution family,
- growth rate,
- Barbashin type theorem,
- nonuniform exponential dichotomy,
- nonuniform polynomial dichotomy
Citation: Tian Yue. Barbashin type characterizations for nonuniform h-dichotomy of evolution families[J]. AIMS Mathematics, 2023, 8(11): 26357-26371. doi: 10.3934/math.20231345

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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.

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