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

Author

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  • Berezansky, Leonid
  • Diblík, Josef
  • Domoshnitsky, Alexander
  • Šmarda, Zdeněk

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.

Suggested Citation

  • Berezansky, Leonid & Diblík, Josef & Domoshnitsky, Alexander & Šmarda, Zdeněk, 2025. "Boundedness of solutions and exponential stability for linear neutral differential systems with Volterra integral part," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p1:s0960077925009750
    DOI: 10.1016/j.chaos.2025.116962
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    References listed on IDEAS

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    1. Cemil Tunç & Fahir Talay Akyildiz & Valerii Obukhovskii, 2024. "Improved Stability and Instability Results for Neutral Integro-Differential Equations including Infinite Delay," Journal of Mathematics, Hindawi, vol. 2024, pages 1-13, June.
    2. Berezansky, Leonid & Diblík, Josef & Svoboda, Zdeněk & Šmarda, Zdeněk, 2015. "Simple uniform exponential stability conditions for a system of linear delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 605-614.
    3. Michael Gil’, 2014. "Stability of Neutral Type Vector Functional Differential Equations with Small Principal Terms," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Mathematics Without Boundaries, edition 127, pages 287-338, Springer.
    4. Ziad Zahreddine, 2003. "Matrix measure and application to stability of matrices and interval dynamical systems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-11, January.
    5. Berezansky, Leonid & Braverman, Elena, 2019. "On stability of linear neutral differential equations in the Hale form," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 63-71.
    Full references (including those not matched with items on IDEAS)

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