Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space

Let Bj(t) (j = 1,..., m) and B(t, τ) (t ≥ 0, 0 ≤ τ ≤ 1) be bounded variable operators in a Banach space. We consider the equation u′(t)=∑k=1mBk(t)u(t-hk(t))+∫01B(t,τ)u(t-h0(τ))dτ (t≥0),u'\left( t \right) = \sum\limits_{k = 1}^m {{B_k}\left( t \right)u\left( {t - {h_k}\left( t \right)} \right...

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Autor principal:	Gil’ Michael
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	differential-delay equations in a banach space stability integro-differential equations 34k30 34k06 34k20 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7ff62461f42b480fa465f123c93c538d
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spelling	oai:doaj.org-article:7ff62461f42b480fa465f123c93c538d2021-12-05T14:10:56ZDelay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space2353-062610.1515/msds-2020-0132https://doaj.org/article/7ff62461f42b480fa465f123c93c538d2021-06-01T00:00:00Zhttps://doi.org/10.1515/msds-2020-0132https://doaj.org/toc/2353-0626Let Bj(t) (j = 1,..., m) and B(t, τ) (t ≥ 0, 0 ≤ τ ≤ 1) be bounded variable operators in a Banach space. We consider the equation u′(t)=∑k=1mBk(t)u(t-hk(t))+∫01B(t,τ)u(t-h0(τ))dτ (t≥0),u'\left( t \right) = \sum\limits_{k = 1}^m {{B_k}\left( t \right)u\left( {t - {h_k}\left( t \right)} \right)} + \int\limits_0^1 {B\left( {t,\tau } \right)u\left( {t - {h_0}\left( \tau \right)} \right)d\tau \,\,\,\,\left( {t \ge 0} \right),} where hk(t) (t ≥ 0; k = 1, ..., m) and h0(τ) are continuous nonnegative bounded functions. Explicit delay-dependent exponential stability conditions for that equation are established. Applications to integro-differential equations with delay are also discussedGil’ MichaelDe Gruyterarticledifferential-delay equations in a banach spacestabilityintegro-differential equations34k3034k0634k20MathematicsQA1-939ENNonautonomous Dynamical Systems, Vol 8, Iss 1, Pp 168-179 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	differential-delay equations in a banach space stability integro-differential equations 34k30 34k06 34k20 Mathematics QA1-939
spellingShingle	differential-delay equations in a banach space stability integro-differential equations 34k30 34k06 34k20 Mathematics QA1-939 Gil’ Michael Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space
description	Let Bj(t) (j = 1,..., m) and B(t, τ) (t ≥ 0, 0 ≤ τ ≤ 1) be bounded variable operators in a Banach space. We consider the equation u′(t)=∑k=1mBk(t)u(t-hk(t))+∫01B(t,τ)u(t-h0(τ))dτ (t≥0),u'\left( t \right) = \sum\limits_{k = 1}^m {{B_k}\left( t \right)u\left( {t - {h_k}\left( t \right)} \right)} + \int\limits_0^1 {B\left( {t,\tau } \right)u\left( {t - {h_0}\left( \tau \right)} \right)d\tau \,\,\,\,\left( {t \ge 0} \right),} where hk(t) (t ≥ 0; k = 1, ..., m) and h0(τ) are continuous nonnegative bounded functions. Explicit delay-dependent exponential stability conditions for that equation are established. Applications to integro-differential equations with delay are also discussed
format	article
author	Gil’ Michael
author_facet	Gil’ Michael
author_sort	Gil’ Michael
title	Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space
title_short	Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space
title_full	Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space
title_fullStr	Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space
title_full_unstemmed	Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space
title_sort	delay-dependent stability conditions for non-autonomous functional differential equations with several delays in a banach space
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/7ff62461f42b480fa465f123c93c538d
work_keys_str_mv	AT gilmichael delaydependentstabilityconditionsfornonautonomousfunctionaldifferentialequationswithseveraldelaysinabanachspace
_version_	1718371550427611136

Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space

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