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Stability and Asymptotically Periodic Solutions of Hybrid Systems with Aftereffect

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In this paper, we study hybrid linear systems of functional differential equations with aftereffect using the W-method proposed by N. V. Azbelev. Two model equations are considered. We examine Banach spaces of right-hand sides and solutions of the equations considered; these spaces consist of asymptotically periodic functions. Analogs of the Bohl–Perron theorem on the asymptotic stability and on the existence of limits of solutions are obtained.

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  1. Perm State National Research University, Perm, Russia

    P. M. Simonov

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  1. P. M. Simonov
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Correspondence to P. M. Simonov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 168, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part I, 2019.

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Simonov, P.M. Stability and Asymptotically Periodic Solutions of Hybrid Systems with Aftereffect. J Math Sci 262, 855–862 (2022). https://doi.org/10.1007/s10958-022-05864-2

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