Abstract:
In the paper we consider a system of linear differential equations of neutral type with periodic coefficients and with distributed delay. Sufficient conditions for the exponential stability of the zero solution of this system are given, estimates for solutions that characterize the exponential decrease at infinity are indicated. In the study of exponential stability, the modified Lyapunov–Krasovskii functional is used. Also for system of delay difference equations, a criterion for the exponential stability of the zero solution in terms of the solvability of the matrix equation with a delayed argument is proved.
Citation:
T. Yskak, “Estimates for solutions of one class of systems of equations of neutral type with distributed delay”, Sib. Èlektron. Mat. Izv., 17 (2020), 416–427
\Bibitem{Ysk20}
\by T.~Yskak
\paper Estimates for solutions of one class of systems of equations of neutral type with distributed delay
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 416--427
\mathnet{http://mi.mathnet.ru/semr1221}
\crossref{https://doi.org/10.33048/semi.2020.17.027}
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https://www.mathnet.ru/eng/semr1221
https://www.mathnet.ru/eng/semr/v17/p416
This publication is cited in the following 8 articles:
I. I. Matveeva, “Estimates of Solutions for a Class of Nonautonomous Systems of Neutral Type with Concentrated and Distributed Delays”, Comput. Math. and Math. Phys., 64:8 (2024), 1796
T. K. Iskakov, “Ustoichivost reshenii sistem lineinykh differentsialnykh uravnenii neitralnogo tipa s beskonechnym raspredelennym zapazdyvaniem”, Chelyab. fiz.-matem. zhurn., 9:4 (2024), 573–584
M. A. Skvortsova, T. Yskak, “Otsenki reshenii differentsialnykh uravnenii s raspredelennym zapazdyvaniem, opisyvayuschikh konkurentsiyu neskolkikh vidov mikroorganizmov”, Sib. zhurn. industr. matem., 25:4 (2022), 193–205
M. A. Skvortsova, “Otsenki reshenii dlya odnoi biologicheskoi modeli”, Matem. tr., 25:1 (2022), 152–176
M. A. Skvortsova, T. Yskak, “Estimates of Solutions to Differential Equations with Distributed Delay Describing the Competition of Several Types of Microorganisms”, J. Appl. Ind. Math., 16:4 (2022), 800
M. A. Skvortsova, T. Yskak, “Asymptotic behavior of solutions in one predator–prey model with delay”, Siberian Math. J., 62:2 (2021), 324–336
M. A. Skvortsova, “Asymptotic properties of solutions to delay differential equations describing plankton-fish interaction”, Mathematics, 9:23 (2021), 3064
T. Yskak, “Stability of Solutions to One Class of Neutral Type Systems of Linear Autonomous Equations with Distributed Delay”, Lobachevskii J Math, 42:14 (2021), 3561
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