Abstract
In this paper, we study systems of nonlinear, nonautonomous, ordinary differential equations that appear in the theory of averaging of nonlinear oscillations. We prove existence theorems for them and obtain conditions under which variables of the type of amplitude (or energy) are uniformly bounded with respect to time.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 85, Proceedings of the International Conference on Differential Equations and Dynamical Systems (Suzdal, June 26–July 2, 2008), 2012.
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Kalyakin, L.A. Existence Theorems and Estimates of Solutions for Equations of Principal Resonance. J Math Sci 200, 82–95 (2014). https://doi.org/10.1007/s10958-014-1906-z
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DOI: https://doi.org/10.1007/s10958-014-1906-z