Boundedness of solutions and exponential stability for linear neutral differential systems with Volterra integral part

Leonid Berezansky; Josef Diblík; Alexander Domoshnitsky; Zdeněk Šmarda

doi:10.1016/j.chaos.2025.116962

Boundedness of solutions and exponential stability for linear neutral differential systems with Volterra integral part

Leonid Berezansky, Josef Diblík, Alexander Domoshnitsky, Zdeněk Šmarda

Department of Mathematics

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

Abstract

A linear vector differential equation with delays, neutral terms and an integral part of Volterra type is considered on the positive semi-axis. The boundedness of all solutions and their exponential stability are investigated. Explicit-type criteria are proved by a method which uses a priori estimates of solutions, the matrix measure, M-matrices, and a generalized Bohl–Perron theorem. Connections with previously known results are discussed. The results are illustrated by examples with problems for further research suggested.

Original language	English
Article number	116962
Journal	Chaos, Solitons and Fractals
Volume	200
DOIs	https://doi.org/10.1016/j.chaos.2025.116962
State	Published - Nov 2025

Keywords

Bohl–Perron theorem
Boundedness
Delay
Exponential stability
Integro-differential equation
Linear neutral system
M-matrix
Matrix measure
Uniform stability
Volterra-type delay
a priori estimates

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10.1016/j.chaos.2025.116962

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title = "Boundedness of solutions and exponential stability for linear neutral differential systems with Volterra integral part",

abstract = "A linear vector differential equation with delays, neutral terms and an integral part of Volterra type is considered on the positive semi-axis. The boundedness of all solutions and their exponential stability are investigated. Explicit-type criteria are proved by a method which uses a priori estimates of solutions, the matrix measure, M-matrices, and a generalized Bohl–Perron theorem. Connections with previously known results are discussed. The results are illustrated by examples with problems for further research suggested.",

keywords = "Bohl–Perron theorem, Boundedness, Delay, Exponential stability, Integro-differential equation, Linear neutral system, M-matrix, Matrix measure, Uniform stability, Volterra-type delay, a priori estimates",

author = "Leonid Berezansky and Josef Dibl{\'i}k and Alexander Domoshnitsky and Zden{\v e}k {\v S}marda",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Ltd",

year = "2025",

month = nov,

doi = "10.1016/j.chaos.2025.116962",

language = "אנגלית",

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T1 - Boundedness of solutions and exponential stability for linear neutral differential systems with Volterra integral part

AU - Berezansky, Leonid

AU - Diblík, Josef

AU - Domoshnitsky, Alexander

AU - Šmarda, Zdeněk

PY - 2025/11

Y1 - 2025/11

N2 - A linear vector differential equation with delays, neutral terms and an integral part of Volterra type is considered on the positive semi-axis. The boundedness of all solutions and their exponential stability are investigated. Explicit-type criteria are proved by a method which uses a priori estimates of solutions, the matrix measure, M-matrices, and a generalized Bohl–Perron theorem. Connections with previously known results are discussed. The results are illustrated by examples with problems for further research suggested.

AB - A linear vector differential equation with delays, neutral terms and an integral part of Volterra type is considered on the positive semi-axis. The boundedness of all solutions and their exponential stability are investigated. Explicit-type criteria are proved by a method which uses a priori estimates of solutions, the matrix measure, M-matrices, and a generalized Bohl–Perron theorem. Connections with previously known results are discussed. The results are illustrated by examples with problems for further research suggested.

KW - Bohl–Perron theorem

KW - Boundedness

KW - Delay

KW - Exponential stability

KW - Integro-differential equation

KW - Linear neutral system

KW - M-matrix

KW - Matrix measure

KW - Uniform stability

KW - Volterra-type delay

KW - a priori estimates

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U2 - 10.1016/j.chaos.2025.116962

DO - 10.1016/j.chaos.2025.116962

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AN - SCOPUS:105012493535

SN - 0960-0779

VL - 200

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

M1 - 116962

ER -

Boundedness of solutions and exponential stability for linear neutral differential systems with Volterra integral part

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