Abstract
We determine a class of multifrequency resonance systems with pulse action for which an integral manifold exists. We construct a function that determines a discontinuous integral manifold and investigate its properties.
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REFERENCES
N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).
Yu. A. Mitropol'skii, A. M. Samoilenko, and N. A. Perestyuk, “Averaging method in impulsive systems,” Ukr. Mat. Zh., 37, No. 1, 56–64 (1985).
A. M. Samoilenko and R. I. Petryshyn, Multifrequency Oscillations of Nonlinear Systems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998).
M. N. Astaf'eva, Averaging of Multifrequency Oscillation Systems with Pulse Action [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Kiev (1989).
Ya. R. Petryshyn, Averaging of Multipoint Problems for Nonlinear Oscillation Systems with Slowly Varying Frequencies [in Ukrainian], Candidate-Degree Thesis (Physics and Mathematics), Kiev (2001).
R. I. Petryshyn and T. M. Sopronyuk, “Exponential estimation of the fundamental matrix of a linear impulsive system,” Ukr. Mat. Zh., 53, No. 8, 1101–1109 (2001).
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Samoilenko, A.M., Petryshyn, R.I. & Sopronyuk, T.M. Construction of an Integral Manifold of a Multifrequency Oscillation System with Fixed Times of Pulse Action. Ukrainian Mathematical Journal 55, 773–800 (2003). https://doi.org/10.1023/B:UKMA.0000010256.56568.d6
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DOI: https://doi.org/10.1023/B:UKMA.0000010256.56568.d6