Geodesic
Stability and asymptotically periodic solutions of hybrid systems with aftereffect
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Tome 168 (2019), pp. 91-98

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In this paper, we study hybrid linear systems of functional differential equations with aftereffect using the Azbelev $W$-method. Two model equations are considered and Banach spaces of right-hand sides and solutions, which are spaces of asymptotically periodic functions, are examined. Analogs of the Bohl–Perron theorem on the asymptotic stability and on the existence of limits of solutions are obtained.
Keywords: Bohl–Perron theorem, asymptotically periodic functions, hybrid system, functional differential equation, equation with aftereffect, stability, method of model equations. 
@article{INTO_2019_168_a10,
     author = {P. M. Simonov},
     title = {Stability and asymptotically periodic solutions of hybrid systems with aftereffect},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {91--98},
     publisher = {mathdoc},
     volume = {168},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_168_a10/}
}
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P. M. Simonov. Stability and asymptotically periodic solutions of hybrid systems with aftereffect. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Tome 168 (2019), pp. 91-98. http://geodesic.mathdoc.fr/item/INTO_2019_168_a10/