Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 782–785 | Cite as

Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces

  • M. V. Falaleev


In this paper, using methods of the theory of generalized functions in Banach spaces, we examine the Cauchy problem for an abstract integrodifferential equation of a specific type. Under the assumption that there exist the complete Jordan structure of the differential part of the equation and the order of the zero of the kernel of the integral part, the fundamental operator-valued function (the fundamental solution) is constructed for the corresponding integrodifferential operator, which is used for further investigation of the problem.


Banach space Fredholm operator generalized function fundamental solution 

AMS Subject Classification

34G10 45K05 45N05 


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  1. 1.
    M. M. Cavalcanti, “Existence and uniform decay for a non-linear viscoelastic equation with strong damping,” Math. Methods Appl. Sci., 24, 1043–1053 (2001).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    M. V. Falaleev, “Singular integrodifferential equations of a specific form in Banach spaces and their applications,” Izv. Irkut. Univ. Ser. Mat., 6, No. 4, 128–137 (2013).zbMATHGoogle Scholar
  3. 3.
    M. M. Vainberg, Theory of Branching of Solutions to Nonlinear Equations [in Russian], Nauka, Moscow (1969).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Irkutsk State UniversityIrkutskRussia

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