Floquet theory and stability for a class of first order differential equations with delays

Alexander Domoshnitsky; Elnatan Berenson; Shai Levi; Elena Litsyn

doi:10.1515/gmj-2023-2119

Floquet theory and stability for a class of first order differential equations with delays

Alexander Domoshnitsky, Elnatan Berenson, Shai Levi, Elena Litsyn

Department of Mathematics

Ariel University

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

Abstract

A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov-Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions.

Original language	English
Pages (from-to)	757-772
Number of pages	16
Journal	Georgian Mathematical Journal
Volume	31
Issue number	5
DOIs	https://doi.org/10.1515/gmj-2023-2119
State	Published - 1 Oct 2024

Keywords

Floquet theory
comparison theorems
delay differential equations
exponential stability
periodic coefficients and delays

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1515/gmj-2023-2119

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title = "Floquet theory and stability for a class of first order differential equations with delays",

abstract = "A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov-Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions.",

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author = "Alexander Domoshnitsky and Elnatan Berenson and Shai Levi and Elena Litsyn",

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doi = "10.1515/gmj-2023-2119",

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T1 - Floquet theory and stability for a class of first order differential equations with delays

AU - Domoshnitsky, Alexander

AU - Berenson, Elnatan

AU - Levi, Shai

AU - Litsyn, Elena

PY - 2024/10/1

Y1 - 2024/10/1

N2 - A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov-Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions.

AB - A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov-Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions.

KW - Floquet theory

KW - comparison theorems

KW - delay differential equations

KW - exponential stability

KW - periodic coefficients and delays

UR - http://www.scopus.com/inward/record.url?scp=85181470436&partnerID=8YFLogxK

U2 - 10.1515/gmj-2023-2119

DO - 10.1515/gmj-2023-2119

M3 - مقالة

SN - 1072-947X

VL - 31

SP - 757

EP - 772

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

IS - 5

ER -

Floquet theory and stability for a class of first order differential equations with delays

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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