Barbashin type characterizations for the uniform polynomial stability and instability of evolution families-Reference-Cited by-同舟云学术

Barbashin type characterizations for the uniform polynomial stability and instability of evolution families

Published:2022-09-23 Issue:6 Volume:29 Page:953-966
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Yue Tian¹^ORCID

Affiliation:

1. School of Mathematics, Physics and Optoelectronic Engineering , Hubei University of Automotive Technology , Shiyan 442002 , P. R. China

Abstract

Abstract The aim of this paper is to give some discrete and continuous versions of Barbashin type theorems for the uniform polynomial stability and instability of evolution families in Banach spaces, by using Banach sequence spaces in ℋ ⁢ ( ℕ ≥ 1 )

{\mathcal{H}(\mathbb{N}_{\geq 1})}

and Banach function spaces in ℋ ⁢ ( ℝ ≥ 1 )

{\mathcal{H}(\mathbb{R}_{\geq 1})}

, respectively. Variants for uniform polynomial stability and instability of some well-known results in the exponential stability theory and polynomial stability theory are obtained.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2022-2188/pdf

Reference29 articles.

1. E. A. Barbashin, Introduction to the Theory of Stability (in Russian), Izdat. “Nauka”, Moscow, 1967.

2. L. Barreira and C. Valls, Polynomial growth rates, Nonlinear Anal. 71 (2009), no. 11, 5208–5219.

3. A. J. G. Bento and C. Silva, Stable manifolds for nonuniform polynomial dichotomies, J. Funct. Anal. 257 (2009), no. 1, 122–148.

4. R. Boruga and M. Megan, Datko type characterizations for nonuniform polynomial dichotomy, Carpathian J. Math. 37 (2021), no. 1, 45–51.

5. C. Buşe, M. Megan, M.-S. Prajea and P. Preda, The strong variant of a Barbashin theorem on stability of solutions for non-autonomous differential equations in Banach spaces, Integral Equations Operator Theory 59 (2007), no. 4, 491–500.

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