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

Leonid Berezansky, Josef Diblík, Alexander Domoshnitsky and Zdeněk Šmarda

Chaos, Solitons & Fractals, 2025, vol. 200, issue P1

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: Boundedness; Bohl–Perron theorem; Exponential stability; Uniform stability; Integro-differential equation; Delay; Volterra-type delay; Linear neutral system; Matrix measure; M-matrix; a priori estimates (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:200:y:2025:i:p1:s0960077925009750

DOI: 10.1016/j.chaos.2025.116962

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