Skip to main content
SpringerLink
Log in

Nonlocal Boundary Value Problem for a Nonlinear Fredholm Integro-Differential Equation with Degenerate Kernel

  • Integral Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We obtain a criterion for the unique solvability of a nonlocal boundary value problem for a second-order nonlinear Volterra integro-differential equation with degenerate kernel. Several informative examples are given.

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

Access this article

Log in via an institution

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. Bang, N.D., Chistyakov, V.F., and Chistyakova, V.F., About some properties of degenerate systems of linear integro-differential equations. I, Izv. Irkutsk. Gos. Univ. Ser. Mat., 2015, vol.11, pp. 13–27.

    MATH  Google Scholar 

  2. Bykov, Ya.V., O nekotorykh zadachakh teorii integro-differentsial’nykh uravnenii (On Some Problems of the Theory of Integro-Differential Equations), Frunze: KGU, 1957.

    Google Scholar 

  3. Vainberg, M.M., Integro-differential equations, Itogi Nauki Mat. Anal. Teor. Veroyatn. Regul. 1962, 1964, pp. 5–37.

    MATH  Google Scholar 

  4. Vasil’ev, V.V., To the problem of solving the Cauchy problem for a class of linear integral-differential equations, Izv. Vyssh. Uchebn. Zaved. Mat., 1961, no. 4, pp. 8–24.

    Google Scholar 

  5. Vlasov, V.V. and Perez Ortiz, R., Spectral analysis of integro-differential equations in viscoelasticity and thermal physics, Math. Notes, 2015, vol.98, no. 4, pp. 689–693.

    Article  MathSciNet  MATH  Google Scholar 

  6. Falaleev, M.V., Integro-differential equations with Fredholm operator at the highest-order derivative in Banach space and their applications, Izv. Irkutsk. Gos. Univ. Ser. Mat., 2012, vol.5, no. 2, pp. 90–102.

    MATH  Google Scholar 

  7. Sidorov, N.A., Solution of the Cauchy problem for a class of integro-differential equations with analytic nonlinearities, Differ. Uravn., 1968, vol.4, no. 7, pp. 1309–1316.

    MathSciNet  Google Scholar 

  8. Dzhumabaev, D.S. and Bakirova, E.A., On unique solvability of the boundary value problem for systems of Fredholm integro-differential equations with degenerate kernel, Nonlinear Oscil., 2015, vol.18, no. 4, pp. 489–506.

    MathSciNet  Google Scholar 

  9. Yuldashev, T.K., A certain Fredholm partial integro-differential equation of the third order, Russ. Math., 2015, vol.59, no. 9, pp. 62–66.

    Article  MathSciNet  MATH  Google Scholar 

  10. Yuldashev, T.K., Inverse problem for a nonlinear Benney-Luke type integro-differential equations with degenerate kernel, Russ. Math., 2016, vol.60, no. 9, pp. 53–60.

    Article  MATH  Google Scholar 

  11. Yuldashev, T.K., Mixed problem for pseudoparabolic integro-differential equation with degenerate kernel, Differ. Equations, 2017, vol.53, no. 1, pp. 99–108.

    Article  MathSciNet  MATH  Google Scholar 

  12. Trenogin, V.A., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1980.

    MATH  Google Scholar 

  13. Ushakov, E.I., Staticheskaya ustoichivost’ elektricheskikh tsepei (Static Stability of Electric Circuits), Nobosibirsk: Nauka, 1988.

    Google Scholar 

  14. Cavalcanti, M.M., Domingos Cavalcanti, V.N., and Ferreira, J., Existence and uniform decay for a nonlinear viscoelastic equation with strong damping, Math. Methods Appl. Sci., 2001, vol.24, pp. 1043–1053.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, 660037, Russia

    T. K. Yuldashev

Authors
  1. T. K. Yuldashev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. K. Yuldashev.

Additional information

Original Russian Text © T.K. Yuldashev, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 12, pp. 1687–1694.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuldashev, T.K. Nonlocal Boundary Value Problem for a Nonlinear Fredholm Integro-Differential Equation with Degenerate Kernel. Diff Equat 54, 1646–1653 (2018). https://doi.org/10.1134/S0012266118120108

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266118120108

Search

Navigation