Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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, 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).

Download references

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. F. Ovchar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. A. Bondar.

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Published:

  • Issue Date:

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

Search

Navigation