Abstract
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.
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M. M. Cavalcanti, “Existence and uniform decay for a non-linear viscoelastic equation with strong damping,” Math. Methods Appl. Sci., 24, 1043–1053 (2001).
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).
M. M. Vainberg, Theory of Branching of Solutions to Nonlinear Equations [in Russian], Nauka, Moscow (1969).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.
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Falaleev, M.V. Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces. J Math Sci 230, 782–785 (2018). https://doi.org/10.1007/s10958-018-3789-x
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DOI: https://doi.org/10.1007/s10958-018-3789-x