Stability for linear second order vector integro-differential equations

Leonid Berezansky; Alexander Domoshnitsky

doi:10.1016/j.rinam.2025.100634

Stability for linear second order vector integro-differential equations

Leonid Berezansky
, Alexander Domoshnitsky

Department of Mathematics

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

Abstract

Explicit sufficient conditions for uniform exponential stability of two-dimensional linear vector integro-differential equations have been established. These criteria are novel and remain valid even in the special case of second-order linear ordinary vector differential equations. The proofs leverage the Bohl–Perron theorem, incorporate a priori estimates of solutions. An illustrative example is provided to demonstrate the applicability of the results.

Original language	English
Article number	100634
Journal	Results in Applied Mathematics
Volume	27
DOIs	https://doi.org/10.1016/j.rinam.2025.100634
State	Published - 1 Aug 2025

Keywords

Bohl–Perron theorem
Integro-differential equations of the second order
Method of a priori estimation
Uniform exponential stability

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.rinam.2025.100634

Cite this

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title = "Stability for linear second order vector integro-differential equations",

abstract = "Explicit sufficient conditions for uniform exponential stability of two-dimensional linear vector integro-differential equations have been established. These criteria are novel and remain valid even in the special case of second-order linear ordinary vector differential equations. The proofs leverage the Bohl{\textendash}Perron theorem, incorporate a priori estimates of solutions. An illustrative example is provided to demonstrate the applicability of the results.",

keywords = "Bohl{\textendash}Perron theorem, Integro-differential equations of the second order, Method of a priori estimation, Uniform exponential stability",

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AU - Domoshnitsky, Alexander

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N2 - Explicit sufficient conditions for uniform exponential stability of two-dimensional linear vector integro-differential equations have been established. These criteria are novel and remain valid even in the special case of second-order linear ordinary vector differential equations. The proofs leverage the Bohl–Perron theorem, incorporate a priori estimates of solutions. An illustrative example is provided to demonstrate the applicability of the results.

AB - Explicit sufficient conditions for uniform exponential stability of two-dimensional linear vector integro-differential equations have been established. These criteria are novel and remain valid even in the special case of second-order linear ordinary vector differential equations. The proofs leverage the Bohl–Perron theorem, incorporate a priori estimates of solutions. An illustrative example is provided to demonstrate the applicability of the results.

KW - Bohl–Perron theorem

KW - Integro-differential equations of the second order

KW - Method of a priori estimation

KW - Uniform exponential stability

UR - https://www.scopus.com/pages/publications/105015468350

U2 - 10.1016/j.rinam.2025.100634

DO - 10.1016/j.rinam.2025.100634

M3 - Article

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VL - 27

JO - Results in Applied Mathematics

JF - Results in Applied Mathematics

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ER -

Stability for linear second order vector integro-differential equations

Abstract

Keywords

ASJC Scopus subject areas

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