Abstract
By using averages of functions, we construct the integral manifold of an oscillating system that passes through resonances in the course of its evolution. We investigate the smoothness of the integral manifold and obtain estimates for its partial derivatives.
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References
A. M. Samoilenko and R. I. Petryshyn, “On the integral manifolds of multifrequency oscillating systems,” Izv. Akad. Nauk SSSR, Ser. Mat., 54, No. 2, 378–395 (1990).
R. I. Petryshyn, Investigation of Oscillating Systems with Slowly Varying Frequencies bx the Averaging Method [in Ukrainian], Doctoral-Degree Thesis (Physics and Mathematics), Kiev (1995).
V. A. Pliss, Integral Sets for Periodic Systems of Differential Equations [in Russian], Nauka, Moscow (1977).
S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Vysshaya Shkola, Moscow (1977).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 1, pp. 87–93, January, 1998.
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Petryshyn, R.I., Lakusta, L.M. On integral manifolds of oscillating systems with slowly varying frequencies. Ukr Math J 50, 100–107 (1998). https://doi.org/10.1007/BF02514691
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DOI: https://doi.org/10.1007/BF02514691