Advertisement

Journal of Mathematical Sciences

, Volume 238, Issue 3, pp 224–235 | Cite as

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

  • I. A. BondarEmail author
  • R. F. Ovchar
Article
  • 1 Downloads

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems, 2nd edition, De Gruyter, Berlin (2016).Google Scholar
  2. 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).Google Scholar
  3. 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).Google Scholar
  4. 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).Google Scholar
  5. 5.
    I. Golovatska, “Weakly perturbed boundary-value problems of integrodifferential equations,” Tatra Mt. Math. Publ., 54, 61–71 (2013).MathSciNetzbMATHGoogle Scholar
  6. 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).Google Scholar
  7. 7.
    S. Fučik and A. Kufner, Nonlinear Differential Equations, Elsevier, Amsterdam (1980).Google Scholar
  8. 8.
    S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Vysshaya Shkola, Moscow (1977).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mathematics, Ukrainian National Academy of SciencesKyivUkraine
  2. 2.Ukrainian National University of Biological Resources and Nature ManagementKyivUkraine

Personalised recommendations