Geodesic
On the asymptotic stability of one equation with a discrete retarded argument
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 83-88.

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In this paper, we consider a functional differential equation with a discrete retarded argument, a constant delay, and a term without delay. The problem of the asymptotic stability of this equation is reduced to the problem of studying the spectrum of the operator of shift along trajectories. Simple coefficient necessary conditions for the asymptotic stability of this equation are obtained.
Keywords: functional differential equation, asymptotic stability, discrete retarded argument, hybrid system 
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M. V. Mulyukov. On the asymptotic stability of one equation with a discrete retarded argument. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 83-88. http://geodesic.mathdoc.fr/item/INTO_2024_231_a7/

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