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Averaging method in multipoint problems of the theory of nonlinear oscillations

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Abstract

By using the averaging method, we prove the solvability of multipoint problems for nonlinear oscillation systems and estimate the deviation of solutions of original and averaged problems.

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References

  1. D. D. Bainov and S. D. Milusheva, “On some applications of the averaging method for solution of initial and boundary-value problems for ordinary differential, integro-differential, and differential-functional equations,” in:Proceedings of the VIII International Conference on Nonlinear Oscillations [in Russian], Prague (1978), pp. 771–789.

  2. V. A. Plotnikov,Averaging Method in Control Systems [in Russian], Lybid’, Kiev, Odessa (1992).

    Google Scholar 

  3. A. M. Samoilenko, “On justification of the averaging method for multifrequency oscillating systems,”Differents. Uravn.,23, No. 2, 267–278 (1987).

    Google Scholar 

  4. V. I. Arnol’d,Supplementary Chapters to the Theory of Ordinary Differential Equations [in Russian] Nauka, Moscow 1978.

    MATH  Google Scholar 

  5. M. M. Khapaev,Averaging in the Theory of Stability [in Russian] Nauka, Moscow 1986.

    Google Scholar 

  6. R. I. Petryshyn,Investigations of Oscillating Systems with Slowly Varying Frequencies by the Averaging Method. Author’s Abstract of the Doctoral Degree Thesis (Physics and Mathematics), Kiev (1995).

  7. R. Reissig, G. Sansone, and R. Conti,Qualitative Theorie of Nichtlinearer Differentialgleichungens, Cremenese, Roma 1963.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. M. Samoilenko

  2. Chernovtsy University, Chernovtsy

    Ya. R. Petryshyn

Authors
  1. A. M. Samoilenko
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  2. Ya. R. Petryshyn
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Samoilenko, A.M., Petryshyn, Y.R. Averaging method in multipoint problems of the theory of nonlinear oscillations. Ukr Math J 48, 1241–1250 (1996). https://doi.org/10.1007/BF02383870

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  • DOI: https://doi.org/10.1007/BF02383870

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