On exponential stability of a linear delay differential equation with an oscillating coefficient

Leonid Berezansky; Elena Braverman

doi:10.1016/j.aml.2009.07.007

On exponential stability of a linear delay differential equation with an oscillating coefficient

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

52 Scopus citations

Abstract

New explicit exponential stability conditions are obtained for the nonautonomous linear equation over(x, ̇) (t) + a (t) x (h (t)) = 0, where h (t) ≤ t and a (t) is an oscillating function. We apply the comparison method based on the Bohl-Perron type theorem. Coefficients and delays are not assumed to be continuous. Some real-world applications and several examples are also discussed.

Original language	English
Pages (from-to)	1833-1837
Number of pages	5
Journal	Applied Mathematics Letters
Volume	22
Issue number	12
DOIs	https://doi.org/10.1016/j.aml.2009.07.007
State	Published - 1 Dec 2009

Keywords

Bohl-Perron type theorem
Delay equations
Exponential stability
Oscillating coefficient

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2009.07.007

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title = "On exponential stability of a linear delay differential equation with an oscillating coefficient",

abstract = "New explicit exponential stability conditions are obtained for the nonautonomous linear equation over(x,{\. }) (t) + a (t) x (h (t)) = 0, where h (t) ≤ t and a (t) is an oscillating function. We apply the comparison method based on the Bohl-Perron type theorem. Coefficients and delays are not assumed to be continuous. Some real-world applications and several examples are also discussed.",

keywords = "Bohl-Perron type theorem, Delay equations, Exponential stability, Oscillating coefficient",

author = "Leonid Berezansky and Elena Braverman",

note = "Funding Information: The authors are grateful to the referees for valuable comments and remarks. The first author was partially supported by Israeli Ministry of Absorption. The second author was partially supported by the NSERC Research Grant.",

year = "2009",

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doi = "10.1016/j.aml.2009.07.007",

language = "English",

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TY - JOUR

T1 - On exponential stability of a linear delay differential equation with an oscillating coefficient

AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Funding Information: The authors are grateful to the referees for valuable comments and remarks. The first author was partially supported by Israeli Ministry of Absorption. The second author was partially supported by the NSERC Research Grant.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - New explicit exponential stability conditions are obtained for the nonautonomous linear equation over(x, ̇) (t) + a (t) x (h (t)) = 0, where h (t) ≤ t and a (t) is an oscillating function. We apply the comparison method based on the Bohl-Perron type theorem. Coefficients and delays are not assumed to be continuous. Some real-world applications and several examples are also discussed.

AB - New explicit exponential stability conditions are obtained for the nonautonomous linear equation over(x, ̇) (t) + a (t) x (h (t)) = 0, where h (t) ≤ t and a (t) is an oscillating function. We apply the comparison method based on the Bohl-Perron type theorem. Coefficients and delays are not assumed to be continuous. Some real-world applications and several examples are also discussed.

KW - Bohl-Perron type theorem

KW - Delay equations

KW - Exponential stability

KW - Oscillating coefficient

UR - https://www.scopus.com/pages/publications/70349481995

U2 - 10.1016/j.aml.2009.07.007

DO - 10.1016/j.aml.2009.07.007

M3 - Article

AN - SCOPUS:70349481995

SN - 0893-9659

VL - 22

SP - 1833

EP - 1837

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 12

ER -

On exponential stability of a linear delay differential equation with an oscillating coefficient

Abstract

Keywords

ASJC Scopus subject areas

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