On uniform exponential trisplitting for cocycles of linear operators in Banach spaces-Reference-Cited by-同舟云学术

On uniform exponential trisplitting for cocycles of linear operators in Banach spaces

Published:2018-12-01 Issue:2 Volume:56 Page:81-103
ISSN:1841-3307
Container-title:Annals of West University of Timisoara - Mathematics and Computer Science
language:en
Short-container-title:

Author:

Biriş Larisa Elena¹,Mihiţ Claudia Luminiţa¹,Ceauşu Traian¹,Popa Ioan-Lucian²

Affiliation:

1. Department of Mathematics , West University of Timişoara , V. Pârvan Blvd., No. 4 300223 Timişoara Romania

2. Department of Exact Sciences and Engineering , University ”1 Decembrie” 1918 of Alba Iulia , 510009 Alba Iulia , Romania

Abstract

Abstract The aim of this paper is to study the concept of uniform exponential trisplitting for skew-product semiflow in Banach spaces. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. We obtain necessary and sufficient conditions for this concept of Datko’s type. a character-isation in terms of Lyapunov functions is provided. The results are obtained from the point of view of the projector families, i.e. invariant and strongly invariant.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/awutm-2018-0017

Reference22 articles.

1. [1] B. Aulbach, J. Kalkbrenner, Exponential forward splitting for noninvertible difference equation, Comput. Math. Appl.42 (2001), 743-754.10.1016/S0898-1221(01)00194-8

2. [2] L. Barreira, C. Valls, Noninvertible cocycles: robustness and exponential dichotomies, Discrete and Continuous Dynamical Systems32 (2012), 4111-4131.10.3934/dcds.2012.32.4111

3. [3] L.E. Biriş, T. Ceauşu, C.L. Mihiţ, On uniform exponential splitting of variational nonautonomous difference equations in Banach spaces, Recent Progress in Difference Equations, Discrete Dynamical Systems and Applications, submitted.

4. [4] L.E. Biriş, T. Ceauşu, C.L. Mihiţ, I.-L. Popa, Uniform Exponential Trisplitting - A New Criterion for Discrete Skew-Product Semiflows, Electron. J. Qual. Theory Differ. Equ.2019, No. 70 (2019), 1-22.

5. [5] L. Biriş, M. Megan, On a concept of exponential dichotomy for co-cycles of linear operators in Banach spaces, Bull. Math. Soc. Sci. Math. Roumanie, 59 (107), No. 3 (2016), 217-223.