On Stability of Linear Neutral Differential Equations with Variable Delays

Leonid Berezansky; Elena Braverman

doi:10.21136/CMJ.2019.0534-17

On Stability of Linear Neutral Differential Equations with Variable Delays

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

8 Scopus citations

Abstract

We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays x˙ (t) − a(t) x˙ (g(t)) + b(t) x(h(t)) = 0 , where | a(t) | < 1 , b(t) ⩾ 0 , h(t) ⩽ t, g(t) ⩽ t, and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.

Original language	English
Pages (from-to)	863-891
Number of pages	29
Journal	Czechoslovak Mathematical Journal
Volume	69
Issue number	3
DOIs	https://doi.org/10.21136/CMJ.2019.0534-17
State	Published - 1 Sep 2019

Keywords

34K06
34K20
34K40
45J05
distributed delay
exponential stability
integro-differential equation
neutral equation
solution estimate

ASJC Scopus subject areas

General Mathematics

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10.21136/CMJ.2019.0534-17

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title = "On Stability of Linear Neutral Differential Equations with Variable Delays",

abstract = "We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays x˙ (t) − a(t) x˙ (g(t)) + b(t) x(h(t)) = 0 , where | a(t) | < 1 , b(t) ⩾ 0 , h(t) ⩽ t, g(t) ⩽ t, and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.",

keywords = "34K06, 34K20, 34K40, 45J05, distributed delay, exponential stability, integro-differential equation, neutral equation, solution estimate",

author = "Leonid Berezansky and Elena Braverman",

note = "Publisher Copyright: {\textcopyright} 2019, Mathematical Institute, Academy of Sciences of Cz.",

year = "2019",

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doi = "10.21136/CMJ.2019.0534-17",

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T1 - On Stability of Linear Neutral Differential Equations with Variable Delays

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AU - Braverman, Elena

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays x˙ (t) − a(t) x˙ (g(t)) + b(t) x(h(t)) = 0 , where | a(t) | < 1 , b(t) ⩾ 0 , h(t) ⩽ t, g(t) ⩽ t, and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.

AB - We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays x˙ (t) − a(t) x˙ (g(t)) + b(t) x(h(t)) = 0 , where | a(t) | < 1 , b(t) ⩾ 0 , h(t) ⩽ t, g(t) ⩽ t, and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.

KW - 34K06

KW - 34K20

KW - 34K40

KW - 45J05

KW - distributed delay

KW - exponential stability

KW - integro-differential equation

KW - neutral equation

KW - solution estimate

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DO - 10.21136/CMJ.2019.0534-17

M3 - Article

AN - SCOPUS:85065388216

SN - 0011-4642

VL - 69

SP - 863

EP - 891

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

IS - 3

ER -

On Stability of Linear Neutral Differential Equations with Variable Delays

Abstract

Keywords

ASJC Scopus subject areas

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