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On the second Bogolyubov theorem for systems with random perturbations

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Abstract

For systems of differential equations with random right-hand sides, we establish conditions for the existence of periodic solutions in the neighborhoods of equilibrium points of the averaged system.

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References

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

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  3. E. F. Tsar'kov,Random Perturbations of Functional-Differential Equations [in Russian], Zinatne, Riga (1989).

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Authors and Affiliations

  1. Kiev University, Kiev

    A. N. Stanzhitskii

Authors
  1. A. N. Stanzhitskii
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1104–1109, August, 1994.

This work was supported by the Ukrainian State Committee on Science and Technology.

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Stanzhitskii, A.N. On the second Bogolyubov theorem for systems with random perturbations. Ukr Math J 46, 1215–1221 (1994). https://doi.org/10.1007/BF01056185

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  • DOI: https://doi.org/10.1007/BF01056185

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