Solution estimates and stability tests for linear neutral differential equations

Leonid Berezansky; Elena Braverman

doi:10.1016/j.aml.2020.106515

Solution estimates and stability tests for linear neutral differential equations

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

3 Scopus citations

Abstract

Explicit exponential stability tests are obtained for the scalar neutral differential equation ẋ(t)−a(t)ẋ(g(t))=−∑k=1mb_k(t)x(h_k(t)), together with exponential estimates for its solutions. Estimates for solutions of a non-homogeneous neutral equation are also obtained, they are valid on every finite segment, thus describing both asymptotic and transient behavior. For neutral differential equations, exponential estimates are obtained here for the first time. Both the coefficients and the delays are assumed to be measurable, not necessarily continuous functions.

Original language	English
Article number	106515
Journal	Applied Mathematics Letters
Volume	108
DOIs	https://doi.org/10.1016/j.aml.2020.106515
State	Published - 1 Oct 2020

Keywords

Explicit solution estimates
Exponential stability tests
Linear neutral differential equations
Variable delays and coefficients

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2020.106515

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title = "Solution estimates and stability tests for linear neutral differential equations",

abstract = "Explicit exponential stability tests are obtained for the scalar neutral differential equation ẋ(t)−a(t)ẋ(g(t))=−∑k=1mbk(t)x(hk(t)), together with exponential estimates for its solutions. Estimates for solutions of a non-homogeneous neutral equation are also obtained, they are valid on every finite segment, thus describing both asymptotic and transient behavior. For neutral differential equations, exponential estimates are obtained here for the first time. Both the coefficients and the delays are assumed to be measurable, not necessarily continuous functions.",

keywords = "Explicit solution estimates, Exponential stability tests, Linear neutral differential equations, Variable delays and coefficients",

author = "Leonid Berezansky and Elena Braverman",

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AU - Braverman, Elena

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N2 - Explicit exponential stability tests are obtained for the scalar neutral differential equation ẋ(t)−a(t)ẋ(g(t))=−∑k=1mbk(t)x(hk(t)), together with exponential estimates for its solutions. Estimates for solutions of a non-homogeneous neutral equation are also obtained, they are valid on every finite segment, thus describing both asymptotic and transient behavior. For neutral differential equations, exponential estimates are obtained here for the first time. Both the coefficients and the delays are assumed to be measurable, not necessarily continuous functions.

AB - Explicit exponential stability tests are obtained for the scalar neutral differential equation ẋ(t)−a(t)ẋ(g(t))=−∑k=1mbk(t)x(hk(t)), together with exponential estimates for its solutions. Estimates for solutions of a non-homogeneous neutral equation are also obtained, they are valid on every finite segment, thus describing both asymptotic and transient behavior. For neutral differential equations, exponential estimates are obtained here for the first time. Both the coefficients and the delays are assumed to be measurable, not necessarily continuous functions.

KW - Explicit solution estimates

KW - Exponential stability tests

KW - Linear neutral differential equations

KW - Variable delays and coefficients

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DO - 10.1016/j.aml.2020.106515

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 106515

ER -

Solution estimates and stability tests for linear neutral differential equations

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Keywords

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