Geodesic
The Bohl--Perron theorem for hybrid linear systems with aftereffect
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 122-126.

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We consider an abstract hybrid system of functional-differential equations. Both equations are functional-differential with respect to one part of variables and difference with respect to to the other part of variables. To the system of two equations with two unknowns appeared, we apply the $W$-method of N. V. Azbelev. We examine two models: a system of functional-differential equations and a system of difference equations. We study the spaces of their solutions and obtain the Bohl–Perron-type theorems on the exponential stability.
Keywords: Bohl–Perron theorem on the exponential stability, hybrid linear system of functional-differential equations, method of model equation. 
@article{INTO_2017_132_a27,
     author = {P. M. Simonov},
     title = {The {Bohl--Perron} theorem for hybrid linear 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 = {122--126},
     publisher = {mathdoc},
     volume = {132},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_132_a27/}
}
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P. M. Simonov. The Bohl--Perron theorem for hybrid linear systems with aftereffect. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 122-126. http://geodesic.mathdoc.fr/item/INTO_2017_132_a27/