Integral Equations and Exponential Trichotomy of Skew-Product Flows

<p>Abstract</p> <p>We are interested in an open problem concerning the integral characterizations of the uniform exponential trichotomy of skew-product flows. We introduce a new admissibility concept which relies on a double solvability of an associated integral equation and prove...

Full description

Bibliographic Details
Main Authors: Sasu AdinaLumini&#355;a, Sasu Bogdan
Format: Article
Language:English
Published: SpringerOpen 2011-01-01
Series:Advances in Difference Equations
Online Access:http://www.advancesindifferenceequations.com/content/2011/918274
id doaj-a036a3127c404d20a68f23ff862f2e2e
record_format Article
spelling doaj-a036a3127c404d20a68f23ff862f2e2e2020-11-24T21:08:13ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472011-01-0120111918274Integral Equations and Exponential Trichotomy of Skew-Product FlowsSasu AdinaLumini&#355;aSasu Bogdan<p>Abstract</p> <p>We are interested in an open problem concerning the integral characterizations of the uniform exponential trichotomy of skew-product flows. We introduce a new admissibility concept which relies on a double solvability of an associated integral equation and prove that this provides several interesting asymptotic properties. The main results will establish the connections between this new admissibility concept and the existence of the most general case of exponential trichotomy. We obtain for the first time necessary and sufficient characterizations for the uniform exponential trichotomy of skew-product flows in infinite-dimensional spaces, using integral equations. Our techniques also provide a nice link between the asymptotic methods in the theory of difference equations, the qualitative theory of dynamical systems in continuous time, and certain related control problems.</p>http://www.advancesindifferenceequations.com/content/2011/918274
collection DOAJ
language English
format Article
sources DOAJ
author Sasu AdinaLumini&#355;a
Sasu Bogdan
spellingShingle Sasu AdinaLumini&#355;a
Sasu Bogdan
Integral Equations and Exponential Trichotomy of Skew-Product Flows
Advances in Difference Equations
author_facet Sasu AdinaLumini&#355;a
Sasu Bogdan
author_sort Sasu AdinaLumini&#355;a
title Integral Equations and Exponential Trichotomy of Skew-Product Flows
title_short Integral Equations and Exponential Trichotomy of Skew-Product Flows
title_full Integral Equations and Exponential Trichotomy of Skew-Product Flows
title_fullStr Integral Equations and Exponential Trichotomy of Skew-Product Flows
title_full_unstemmed Integral Equations and Exponential Trichotomy of Skew-Product Flows
title_sort integral equations and exponential trichotomy of skew-product flows
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1839
1687-1847
publishDate 2011-01-01
description <p>Abstract</p> <p>We are interested in an open problem concerning the integral characterizations of the uniform exponential trichotomy of skew-product flows. We introduce a new admissibility concept which relies on a double solvability of an associated integral equation and prove that this provides several interesting asymptotic properties. The main results will establish the connections between this new admissibility concept and the existence of the most general case of exponential trichotomy. We obtain for the first time necessary and sufficient characterizations for the uniform exponential trichotomy of skew-product flows in infinite-dimensional spaces, using integral equations. Our techniques also provide a nice link between the asymptotic methods in the theory of difference equations, the qualitative theory of dynamical systems in continuous time, and certain related control problems.</p>
url http://www.advancesindifferenceequations.com/content/2011/918274
work_keys_str_mv AT sasuadinalumini355a integralequationsandexponentialtrichotomyofskewproductflows
AT sasubogdan integralequationsandexponentialtrichotomyofskewproductflows
_version_ 1716760442080067584