Abstract
For a linear almost periodic system under pulse influence, the conditions are established under which this system is reducible (by a linear change of variables with a discontinuous almost periodic matrix) to a system without pulses but with a Bohr almost periodic right-hand side. The set of linear almost periodic pulse systems possessing only bounded solutions is studied.
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References
A. Halanai and D. Veksler,Qualitative Theory of Pulse Systems [Russian translation], Mir, Moscow (1971).
A. M. Samoilenko and N. A. Perestyuk,Differential Equations under Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).
A. M. Samoilenko, N. A. Perestyuk, and M. U. Akhmetov,Almost Periodic Solutions of Differential Equations under Pulse Influence [in Russian], Preprint, Institute of Mathematics, Ukrainian Academy of Sciences, No. 26, Kiev (1983).
F. R. Gantmakher,Theory of Matrices [in Russian], Nauka, Moscow (1988).
A. M. Samoilenko,Elements of Mathematical Theory of Multifrequence Oscillations. Invariant Tori [in Russian], Nauka, Moscow (1987).
B. M. Levitan,Almost Periodic Functions [in Russian], Gostekhizdat, Moscow (1953).
J. Kurzweil and A. Velkovska, “On linear differential equations with almost periodic coefficients and property that the unit sphere is invariant,”Lect. Notes Math.,1017, 364–368 (1983).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 105–113, January, 1993.
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Tkachenko, V.I. On linear almost periodic pulse systems. Ukr Math J 45, 116–125 (1993). https://doi.org/10.1007/BF01062044
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DOI: https://doi.org/10.1007/BF01062044