Stability of linear differential equations with a distributed delay

Leonid Berezansky; Elena Braverman

doi:10.3934/cpaa.2011.10.1361

Stability of linear differential equations with a distributed delay

Leonid Berezansky
, Elena Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We present some new stability results for the scalar linear equation with a distributed delay x(t)+σ^m_k=1∫^t _hk(t)x(s)d_sR_k(t,s)=0,h_k(t)≤t,sup _t≤0(t-h_k(t)) < ∞, where the functions involved in the equation are not required to be continuous. The results are applied to integro-differential equations, equations with several concentrated delays and equations of a mixed type.

Original language	English
Pages (from-to)	1361-1375
Number of pages	15
Journal	Communications on Pure and Applied Analysis
Volume	10
Issue number	5
DOIs	https://doi.org/10.3934/cpaa.2011.10.1361
State	Published - 1 Sep 2011

Keywords

Distributed delay
Explicit stability conditions
Exponential stability

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2011.10.1361

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abstract = "We present some new stability results for the scalar linear equation with a distributed delay x(t)+σmk=1∫t hk(t)x(s)dsRk(t,s)=0,hk(t)≤t,sup t≤0(t-hk(t)) < ∞, where the functions involved in the equation are not required to be continuous. The results are applied to integro-differential equations, equations with several concentrated delays and equations of a mixed type.",

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AU - Braverman, Elena

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N2 - We present some new stability results for the scalar linear equation with a distributed delay x(t)+σmk=1∫t hk(t)x(s)dsRk(t,s)=0,hk(t)≤t,sup t≤0(t-hk(t)) < ∞, where the functions involved in the equation are not required to be continuous. The results are applied to integro-differential equations, equations with several concentrated delays and equations of a mixed type.

AB - We present some new stability results for the scalar linear equation with a distributed delay x(t)+σmk=1∫t hk(t)x(s)dsRk(t,s)=0,hk(t)≤t,sup t≤0(t-hk(t)) < ∞, where the functions involved in the equation are not required to be continuous. The results are applied to integro-differential equations, equations with several concentrated delays and equations of a mixed type.

KW - Distributed delay

KW - Explicit stability conditions

KW - Exponential stability

UR - https://www.scopus.com/pages/publications/82155191438

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JO - Communications on Pure and Applied Analysis

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IS - 5

ER -

Stability of linear differential equations with a distributed delay

Abstract

Keywords

ASJC Scopus subject areas

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