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Bifurcation of Solutions of the Boundary-Value Problem for Systems of Integrodifferential Equations with Degenerate Kernel

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We establish sufficient conditions for the existence of solutions of a weakly perturbed linear boundary-value problems for a system of integrodifferential equations. We also establish conditions for the existence and uniqueness of solutions of problems of this kind and propose an iterative procedure for the construction of the required solutions.

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References

  1. A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, 2nd edition, De Gruyter, Berlin (2016).

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

  3. A. M. Samoilenko, A. A. Boichuk, and S. A. Krivosheya, “Boundary-value problems for systems of integrodifferential equations with degenerate kernel,” Ukr. Mat. Zh., 48, No. 11, 1576–1579 (1996); English translation: Ukr. Math. J., 48, No. 11, 1785–1789 (1996).

  4. I. A. Holovats’ka, “Weakly perturbed systems of linear integrodifferential equations,” Nelin. Kolyv., 15, No. 2, 151–164 (2012); English translation: J. Math. Sci., 189, No. 5, 735–750 (2013).

  5. I. Golovatska, “Weakly perturbed boundary-value problems of integrodifferential equations,” Tatra Mt. Math. Publ., 54, 61–71 (2013).

    MathSciNet  MATH  Google Scholar 

  6. M. I. Vishik and L. A. Lyusternik, “Solution of some perturbed problems in the case of matrices and self-adjoint and nonself-adjoint differential equations,” Usp. Mat. Nauk, 15, Issue 3, 3–80 (1960).

  7. S. Fučik and A. Kufner, Nonlinear Differential Equations, Elsevier, Amsterdam (1980).

  8. S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Vysshaya Shkola, Moscow (1977).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivs’ka Str., 3, Kyiv, 01004, Ukraine

    I. A. Bondar

  2. Ukrainian National University of Biological Resources and Nature Management, Heroiv Oborony Str., 15, Kyiv, 03041, Ukraine

    R. F. Ovchar

Authors
  1. I. A. Bondar
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  2. R. F. Ovchar
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Correspondence to I. A. Bondar.

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Translated from Neliniini Kolyvannya, Vol. 20, No. 4, pp. 465–476, October–December, 2017.

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Bondar, I.A., Ovchar, R.F. Bifurcation of Solutions of the Boundary-Value Problem for Systems of Integrodifferential Equations with Degenerate Kernel. J Math Sci 238, 224–235 (2019). https://doi.org/10.1007/s10958-019-04231-y

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  • DOI: https://doi.org/10.1007/s10958-019-04231-y

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