Skip to main content
SpringerLink
Log in

Domain of convergence of an iterative procedure for an autonomous boundary-value problem

  • Published:
Nonlinear Oscillations

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We find an estimate for the range of values of a small parameter for which the convergence of an iterative procedure for the construction of solutions of an autonomous weakly nonlinear Noether boundary-value problem for a system of ordinary differential equations in the critical case is preserved.

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. A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, VSP, Utrecht (2004).

    MATH  Google Scholar 

  2. E. A. Grebenikov and Yu. A. Ryabov, Constructive Methods for Analysis of Nonlinear Systems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  3. A. A. Boichuk, Constructive Methods for Analysis of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

  4. O. B. Lykova and A. A. Boichuk, “Construction of periodic solutions of nonlinear systems in critical cases,” Ukr. Mat. Zh., 40, No. 1, 62–69 (1988).

    Article  MathSciNet  Google Scholar 

  5. A. S. Chuiko, “Domain of convergence of an iterative procedure for a weakly nonlinear boundary-value problem,” Nelin. Kolyvannya, 8, No. 2, 278–288 (2005).

    MathSciNet  Google Scholar 

  6. A. A. Boichuk and S. M. Chuiko, “Autonomous weakly nonlinear boundary-value problems,” Differents. Uravn., 28, No. 10, 1668–1674 (1992).

    MathSciNet  Google Scholar 

  7. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  8. I. G. Malkin, Some Problems in the Theory of Nonlinear Oscillations [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  9. S. M. Chuiko, “Green operator of a boundary-value problem with pulse action,” Differents. Uravn., 37, No. 8, 1132–1135 (2001).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Slavyansk Pedagogic University, Slavyansk

    S. M. Chuiko

Authors
  1. S. M. Chuiko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Neliniini Kolyvannya, Vol. 9, No. 3, pp. 416–432, July–September, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chuiko, S.M. Domain of convergence of an iterative procedure for an autonomous boundary-value problem. Nonlinear Oscill 9, 405–422 (2006). https://doi.org/10.1007/s11072-006-0053-y

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11072-006-0053-y

Keywords

Search

Navigation