On stability of linear neutral differential equations in the Hale form

Leonid Berezansky; Elena Braverman

doi:10.1016/j.amc.2018.08.010

On stability of linear neutral differential equations in the Hale form

Leonid Berezansky
, Elena Braverman

Department of Mathematics

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

2 Scopus citations

Abstract

We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays (x(t)−a(t)x(g(t)))^′=−b(t)x(h(t)),where |a(t)| < 1, b(t) ≥ 0, h(t) ≤ t, g(t) ≤ t, in the case when the delays t−h(t), t−g(t) are bounded, as well as an asymptotic stability condition, if the delays can be unbounded.

Original language	English
Pages (from-to)	63-71
Number of pages	9
Journal	Applied Mathematics and Computation
Volume	340
DOIs	https://doi.org/10.1016/j.amc.2018.08.010
State	Published - 1 Jan 2019

Keywords

Asymptotic stability
Exponential stability
Neutral equations in the Hale form
Neutral pantograph equation
Solution estimates
Unbounded delays

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2018.08.010

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title = "On stability of linear neutral differential equations in the Hale form",

abstract = "We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays (x(t)−a(t)x(g(t)))′=−b(t)x(h(t)),where |a(t)| < 1, b(t) ≥ 0, h(t) ≤ t, g(t) ≤ t, in the case when the delays t−h(t), t−g(t) are bounded, as well as an asymptotic stability condition, if the delays can be unbounded.",

keywords = "Asymptotic stability, Exponential stability, Neutral equations in the Hale form, Neutral pantograph equation, Solution estimates, Unbounded delays",

author = "Leonid Berezansky and Elena Braverman",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

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doi = "10.1016/j.amc.2018.08.010",

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T1 - On stability of linear neutral differential equations in the Hale form

AU - Berezansky, Leonid

AU - Braverman, Elena

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays (x(t)−a(t)x(g(t)))′=−b(t)x(h(t)),where |a(t)| < 1, b(t) ≥ 0, h(t) ≤ t, g(t) ≤ t, in the case when the delays t−h(t), t−g(t) are bounded, as well as an asymptotic stability condition, if the delays can be unbounded.

AB - We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays (x(t)−a(t)x(g(t)))′=−b(t)x(h(t)),where |a(t)| < 1, b(t) ≥ 0, h(t) ≤ t, g(t) ≤ t, in the case when the delays t−h(t), t−g(t) are bounded, as well as an asymptotic stability condition, if the delays can be unbounded.

KW - Asymptotic stability

KW - Exponential stability

KW - Neutral equations in the Hale form

KW - Neutral pantograph equation

KW - Solution estimates

KW - Unbounded delays

UR - https://www.scopus.com/pages/publications/85052948955

U2 - 10.1016/j.amc.2018.08.010

DO - 10.1016/j.amc.2018.08.010

M3 - Article

AN - SCOPUS:85052948955

SN - 0096-3003

VL - 340

SP - 63

EP - 71

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

On stability of linear neutral differential equations in the Hale form

Abstract

Keywords

ASJC Scopus subject areas

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