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The Bohl–Perron Theorem for Hybrid Linear Systems with Aftereffect

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Abstract

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.

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References

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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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Dedicated to the memory of Professor N. V. Azbelev and A. V. Chistyakov

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.

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Simonov, P.M. The Bohl–Perron Theorem for Hybrid Linear Systems with Aftereffect. J Math Sci 230, 775–781 (2018). https://doi.org/10.1007/s10958-018-3788-y

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  • DOI: https://doi.org/10.1007/s10958-018-3788-y

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