Abstract
For systems of differential equations with impulse action at nonfixed moments of time, the concept of a generalized solution is presented. On its basis a classification of impulse systems is proposed and conditions are indicated sufficient for the impulse system to belong to one class or another.
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A. M. Samoilenko, N. A. Perestyuk, and S. I. Trofimchuk, The Problem of “Pulsations” in Impulse Systems, Preprint 90.11, Inst. Mat. Akad. Ukr. SSR, Kiev (1990).
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Yu. V. Rogovchenko and S. I. Trofimchuk, “Periodic solutions of weakly nonlinear systems with impulse action,” Ukr. Mat. Zh.,41, No. 5, 622–626 (1989).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 657–663, May, 1991.
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Samoilenko, A.M., Perestyuk, N.A. & Trofimchuk, S.I. Generalized solutions of impulse systems and the phenomenon of pulsations. Ukr Math J 43, 610–615 (1991). https://doi.org/10.1007/BF01058548
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DOI: https://doi.org/10.1007/BF01058548