Ukrainian Mathematical Journal

, Volume 66, Issue 11, pp 1665–1679 | Cite as

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

  • N. D. Kopachevskii
  • E. V. Semkina

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.


Cauchy Problem Strong Solution Operator Versus Operator Matrix Integrodifferential Equation 
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  1. 1.
    N. D. Kopachevskii, Volterra Integrodifferential Equations in Hilbert Spaces. A Special Course of Lectures [in Russian], FLP “Bondarenko O. A.”, Simferopol’ (2012).Google Scholar
  2. 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).Google Scholar
  3. 3.
    V. Poblete, “Solutions of second-order integrodifferential equations on periodic Besov spaces,” Proc. Edinburgh Math. Soc., 50, 477–492 (2007).MathSciNetCrossRefGoogle Scholar
  4. 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).Google Scholar
  5. 5.
    S. Trostorff, “On integrodifferential inclusions with operator-valued kernels,” Math. Meth. Appl. Sci. (2014), doi: 10.1002/mma.3111.Google Scholar
  6. 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).MathSciNetGoogle Scholar
  7. 7.
    T. Diagana, “Existence results for some damped second-order Volterra integrodifferential equations,” Appl. Math. Comput., 237, 304–317 (2014).MathSciNetCrossRefGoogle Scholar
  8. 8.
    S. G. Krein (editor), Functional Analysis [in Russian], Nauka, Moscow (1972).Google Scholar
  9. 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).Google Scholar
  10. 10.
    S. G. Krein, Linear Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1967).Google Scholar
  11. 11.
    S. Ya. Yakubov, Linear Differential-Operator Equations and Their Applications [in Russian], Élm, Baku (1985).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • N. D. Kopachevskii
    • 1
  • E. V. Semkina
    • 1
  1. 1.Vernadskii National Tavrida UniversitySimferopolUkraine

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