Skip to main content
SpringerLink
Log in

Averaging of a multifrequency boundary-value problem with linearly transformed argument

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We establish the existence of a solution and obtain an estimate of the error of the averaging method for a multifrequency system with linearly transformed argument and multipoint boundary conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  2. A. M. Samoilenko and R. I. Petryshyn, Multifrequency Oscillations of Nonlinear Systems [in Ukrainian], Institute of Mathematics. Ukrainian Academy of Sciences, Kiev (1998).

    MATH  Google Scholar 

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

    Google Scholar 

  4. Ya. I. Bigun, “Averaging method in multifrequency systems with delay,” Ukr. Mat. Zh., 50, No. 2, 299–303 (1998).

    Article  MathSciNet  Google Scholar 

  5. N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina. Introduction to the Theory of Functional Differential Equations [in Russian], Nauka. Moscow (1991).

    MATH  Google Scholar 

  6. A. A. Boichuk. V. F. Zhuravlev, and A. M. Samoilenko. Generalized Inverse Operators and Noetherian Boundary-Value Problems [in Russian] Institute of Mathematics, Ukrainian Academy of Sciences, Kiev 1995.

    Google Scholar 

  7. L. D. Akulenko, Asymptotic Methods of Optimal Control [in Russian] Nauka, Moscow 1987.

    MATH  Google Scholar 

  8. V. A. Plotnikov, Averaging Method in Control Problems [in Russian], Lybid’, Kiev (1992).

    Google Scholar 

  9. Yu. A. Mitropol’skii, D. D. Bainov, and S. D. Milusheva, “Application of the averaging method for the solution of boundary-value problems for ordinary differential and integro-differential equations,” Mat. Fiz., No. 25, 3–22 (1979).

    Google Scholar 

  10. A. M. Samoilenko and Kh. Z. Mustafaev, “On the averaging principle for one class of systems of differential equations with deviating argument,” Ukr. Mat. Zh., 42. No. 10. 1363–1369 (1990).

    Article  MathSciNet  Google Scholar 

  11. I. G. Petrovskii, Lectures on the Theory of Ordinary Differential Equations [in Russian] Nauka, Moscow 1970.

    Google Scholar 

  12. M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii. and V. Ya. Stetsenko, Approximate Solution of Operator Equations [in Russian] Nauka, Moscow 1969.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukranian Academy of Sciences, kiev

    Ya. I. Bigun

Authors
  1. Ya. I. Bigun
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bigun, Y.I. Averaging of a multifrequency boundary-value problem with linearly transformed argument. Ukr Math J 52, 335–345 (2000). https://doi.org/10.1007/BF02513129

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02513129

Keywords

Search

Navigation