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Periodic Solutions of Second-Order Differential Equations with Large Parameters

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Abstract

A second-order differential equation containing a large parameter is considered. Such an equation can be interpreted as an equation of constrained oscillations of a mechanical system with one degree of freedom, provided that the fundamental frequency of the system substantially exceeds the external frequency. We provide a new proof of the existence of a periodic solution of that equation such that it is close to the periodic solution of the corresponding degenerate equation. That proof is obtained by means of the Poincaré method.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics of RAS, Moscow, 125047, Russia

    V. V. Sazonov

  2. Moscow State University, Moscow, 119991, Russia

    A. V. Troitskaya

Authors
  1. V. V. Sazonov
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  2. A. V. Troitskaya
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Corresponding author

Correspondence to V. V. Sazonov.

Additional information

Original Russian Text © V.V. Sazonov, A.V. Troitskaya, 2018, published in Prikladnaya Matematika i Mekhanika, 2018, Vol. 82, No. 5, pp. 622–630.

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Sazonov, V.V., Troitskaya, A.V. Periodic Solutions of Second-Order Differential Equations with Large Parameters. Mech. Solids 53 (Suppl 2), 87–94 (2018). https://doi.org/10.3103/S0025654418050151

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  • DOI: https://doi.org/10.3103/S0025654418050151

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