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Weakly nonlinear boundary-value problems for operator equations with pulse influence

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Abstract

We consider the problem of finding conditions of solvability and algorithms for construction of solutions of weakly nonlinear boundary-value problems for operator equations (with the Noetherian linear part) with pulse influence at fixed times. The method of investigation is based on passing by methods of the Lyapunov—Schmidt type from a pulse boundary-value problem to an equivalent operator system that can be solved by iteration procedures based on the fixed-point principle.

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References

  1. A. M. Samoilenko and N. A. Perestyuk, Differential Equations with Pulse Influence, [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  2. A. Halanay and D. Wexler, Qualitative Theory of Pulse Systems [In Romanian], Editura Academiei Rep. Soc. Romania, Bucharest (1968).

    Google Scholar 

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

    MATH  Google Scholar 

  4. A. A. Boichuk, V. F. Zhuravlev, and A. M. Samoilenko, “Linear Noether boundary-value problems for pulse differential systems with lag,” Differents. Uravn., 30, No. 10, 1677–1682 (1994).

    MathSciNet  Google Scholar 

  5. S. G. Krein, Linear Equations in Banach Space [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  6. 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 

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

    MATH  Google Scholar 

  8. L. V. Kantorovich, “Principle of the Lyapunov majorants and the Newton method,” Dokl. Akad Nauk SSSR, 76, No. 1, 17–20 (1951).

    Google Scholar 

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Authors
  1. A. M. Samoilenko
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  2. A. A. Boichuk
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  3. V. F. Zhuravlev
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 272–288, February, 1997.

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Samoilenko, A.M., Boichuk, A.A. & Zhuravlev, V.F. Weakly nonlinear boundary-value problems for operator equations with pulse influence. Ukr Math J 49, 302–319 (1997). https://doi.org/10.1007/BF02486444

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  • DOI: https://doi.org/10.1007/BF02486444

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