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Domain of Convergence of an Iteration Procedure for a Weakly Nonlinear Boundary-Value Problem

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Nonlinear Oscillations

Abstract

We obtain estimates for the values of a small parameter for which the iteration procedure used for the construction of solutions of the Noetherian weakly nonlinear boundary-value problem for a system of ordinary differential equations is convergent in both critical and noncritical cases.

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REFERENCES

  1. 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 

  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).

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  5. F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1988).

    MATH  Google Scholar 

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

    Google Scholar 

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Authors and Affiliations

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

    A. S. Chuiko

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  1. A. S. Chuiko
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Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 278–288, April–June, 2005.

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Chuiko, A.S. Domain of Convergence of an Iteration Procedure for a Weakly Nonlinear Boundary-Value Problem. Nonlinear Oscill 8, 277–287 (2005). https://doi.org/10.1007/s11072-005-0056-0

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  • DOI: https://doi.org/10.1007/s11072-005-0056-0

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