Extending Some Results of L. Barreira and C. Valls to the Case of Linear Skew-Product Semiflows

Extending Some Results of L. Barreira and C. Valls to the Case of Linear Skew-Product Semiflows In a paper from 2010, Barreira and Valls (J Differ Equ 249:2889–2904, 2010) use Lyapunov norms to set up admissibility conditions for nonuniform exponential contractions. In 2011, the same authors extend their analysis from Barreira and Valls (J Differ Equ 249:2889–2904, 2010) to the case of nonuniform exponential dichotomy for linear evolution families with (non)uniform exponential growth (see Barreira and Valls in Discret Contin Dyn Syst 30(1):39–53, 2011). Following their approach, we are able to choose appropriate “test-functions” to establish admissibility-type conditions for the existence of a (non)uniform exponential dichotomy of a strongly continuous cocycle with (non)uniform exponential growth. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

Extending Some Results of L. Barreira and C. Valls to the Case of Linear Skew-Product Semiflows

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-017-0666-8
Publisher site
See Article on Publisher Site

Abstract

In a paper from 2010, Barreira and Valls (J Differ Equ 249:2889–2904, 2010) use Lyapunov norms to set up admissibility conditions for nonuniform exponential contractions. In 2011, the same authors extend their analysis from Barreira and Valls (J Differ Equ 249:2889–2904, 2010) to the case of nonuniform exponential dichotomy for linear evolution families with (non)uniform exponential growth (see Barreira and Valls in Discret Contin Dyn Syst 30(1):39–53, 2011). Following their approach, we are able to choose appropriate “test-functions” to establish admissibility-type conditions for the existence of a (non)uniform exponential dichotomy of a strongly continuous cocycle with (non)uniform exponential growth.

Journal

Results in MathematicsSpringer Journals

Published: Feb 28, 2017

References

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