We establish conditions for the existence of periodic solutions of a system with impulsive action at nonfixed times.
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N. M. Krylov and N. N. Bogolyubov, Introduction to Nonlinear Mechanics [in Russian], Akad. Nauk Ukr. SSR, Kiev (1937).
A. M. Samoilenko, “Averaging method for investigating systems subjected to an impulsive action,” Ukr. Mat. Zh., 19, No. 5, 96–104 (1967); English translation: Ukr. Math. J., 19, No. 5, 586–593 (1967).
A. M. Samoilenko, “Averaging method in systems with pushes,” Mat. Fiz., Issue 9, 63–96 (1971).
A. M. Samoilenko and N. A. Perestyuk, “On the averaging method in systems with impulsive action,” Ukr. Mat. Zh., 26, No. 5, 411–418 (1974).
A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods for the Investigation of Periodic Solutions [in Russian], Vyshcha Shkola, Kiev (1976).
N. A. Perestyuk, V. A. Plotnikov, A. M. Samoilenko, and N. V. Skripnik, Impulsive Differential Equations with Set-Valued and Discontinuous Right-Hand Sides [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2007).
N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1963).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 4, pp. 486–493, April, 2013.
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Ivashchuk, O.V. Periodic solutions of a system with impulsive action at nonfixed times. Ukr Math J 65, 531–540 (2013). https://doi.org/10.1007/s11253-013-0793-7
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DOI: https://doi.org/10.1007/s11253-013-0793-7