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Averaging of differential equations with Perron-integrable right-hand side

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Nonlinear Oscillations

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We consider a generalization of the Bogolyubov theorem to differential equations with Perron-integrable right-hand side.

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References

  1. N. P. Erugin, I. Z. Shtokalo, P. S. Bondarenko, et al., A Course in Ordinary Differential Equations [in Russian], Vyshcha Shkola, Kiev (1974).

    Google Scholar 

  2. A. F. Filippov, Differential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).

    MATH  Google Scholar 

  3. M. M. Khapaev, “On the averaging method in some problems related to averaging,” Differents. Uravn., 11, No. 5, 600–608 (1966).

    Google Scholar 

  4. I. P. Natanson, Theory of Functions of a Real Variable [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  5. S. Saks, Theory of the Integral, PWN, Warsaw (1937).

    Google Scholar 

  6. Yu. A. Mitropol'skii, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).

    Google Scholar 

  7. V. V. Filippov, On the Spaces of Solutions of Ordinary Differential Equations [in Russian], MMF MGU, Moscow (1996).

    Google Scholar 

  8. N. M. Krylov and N. N. Bogolyubov, An Introduction to Nonlinear Mechanics [in Russian], Ukrainian Academy of Sciences, Kiev (1937).

    Google Scholar 

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Correspondence to V. A. Plotnikov.

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Translated from Neliniini Kolyvannya, Vol. 11, No. 3, pp. 387–395, July–September, 2008.

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Plotnikov, V.A., Romanyuk, A.V. Averaging of differential equations with Perron-integrable right-hand side. Nonlinear Oscill 11, 407–415 (2008). https://doi.org/10.1007/s11072-009-0039-7

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  • DOI: https://doi.org/10.1007/s11072-009-0039-7

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