Abstract
Under consideration is the class of nonlinear systems of nonautonomous differential equations of neutral type with a variable delay that can be unbounded. Using a Lyapunov–Krasovskii functional, we establish some estimates of solutions that allow us to conclude whether the solutions are stable. In the case of exponential and asymptotic stability, we estimate the attraction domains and the rate of stabilization of solutions at infinity.
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Acknowledgment
The author is grateful to Professor G. V. Demidenko for useful discussions.
Funding
The author was supported by the Russian Foundation for Basic Research (Grant 18–29–10086).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 3, pp. 583–598. https://doi.org/10.33048/smzh.2021.62.310
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Matveeva, I.I. Estimates for Solutions to a Class of Nonautonomous Systems of Neutral Type with Unbounded Delay. Sib Math J 62, 468–481 (2021). https://doi.org/10.1134/S0037446621030101
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DOI: https://doi.org/10.1134/S0037446621030101
Keywords
- differential equation of neutral type
- variable coefficients
- estimates for solutions
- stability
- Lyapunov–Krasovskii functional