Skip to main content
SpringerLink
Log in

Complete Volterra Integrodifferential Equations of the Second Order Unsolved with Respect to the Higher Derivative

  • Published:
Ukrainian Mathematical Journal Aims and scope

We prove the theorem on solvability of the Cauchy problem for the complete Volterra integrodifferential linear equations of the second order in a Hilbert space. For a complete equation, we consider three main classes of equations depending on the ordering of operator coefficients.

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. N. D. Kopachevskii, Volterra Integrodifferential Equations in Hilbert Spaces. A Special Course of Lectures [in Russian], FLP “Bondarenko O. A.”, Simferopol’ (2012).

  2. V. V. Vlasov, D. A. Medvedev, and N. A. Rautian, “Functional-differential equations in Sobolev spaces and their spectral analysis,” Sovr. Probl. Mat. Mekh., Mat., 8, Issue 1, 8–306 (2011).

  3. V. Poblete, “Solutions of second-order integrodifferential equations on periodic Besov spaces,” Proc. Edinburgh Math. Soc., 50, 477–492 (2007).

    Article  MathSciNet  Google Scholar 

  4. R. Alikhani, F. Bahrami, and A. Jabbari, “Existence of global solutions to nonlinear fuzzy Volterra integrodifferential equations,” in: Nonlin. Anal.: Theory, Meth. Appl., 75, 1810–1821 (2012).

  5. S. Trostorff, “On integrodifferential inclusions with operator-valued kernels,” Math. Meth. Appl. Sci. (2014), doi: 10.1002/mma.3111.

    Google Scholar 

  6. V. Vlasov and N. Rautian, “Spectral analysis and representations of solutions of abstract integrodifferential equations in Hilbert space,” Operator Theory: Adv. Appl., 236, 517–535 (2014).

    MathSciNet  Google Scholar 

  7. T. Diagana, “Existence results for some damped second-order Volterra integrodifferential equations,” Appl. Math. Comput., 237, 304–317 (2014).

    Article  MathSciNet  Google Scholar 

  8. S. G. Krein (editor), Functional Analysis [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  9. M. Sh. Birman and M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in Hilbert Spaces, [in Russian], 2nd Edn., Lan’, St.-Petersburg (2010).

  10. S. G. Krein, Linear Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  11. S. Ya. Yakubov, Linear Differential-Operator Equations and Their Applications [in Russian], Élm, Baku (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vernadskii National Tavrida University, Simferopol, Ukraine

    N. D. Kopachevskii & E. V. Semkina

Authors
  1. N. D. Kopachevskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Semkina
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 11, pp. 1485–1497, November, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kopachevskii, N.D., Semkina, E.V. Complete Volterra Integrodifferential Equations of the Second Order Unsolved with Respect to the Higher Derivative. Ukr Math J 66, 1665–1679 (2015). https://doi.org/10.1007/s11253-015-1043-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-015-1043-y

Keywords

Search

Navigation