We establish the existence and uniqueness of a generalized solution to the Cauchy problem for the Barbashin integro-differential equation and a system of such equations. The results are illustrated by examples. Bibliography: 6 titles.
Similar content being viewed by others
References
J. M. Appell, A. S. Kalitvin, and P. P. Zabrejko, Partial Integral Operators and Integro-Differential Equations, Marcel Dekker, New York (2000).
G. Brack, “Systems with substantially distributed parameters,” Math. Res. 27, 421–424 (1985).
A. S. Kalitvin, “Some aspects of the theory of integro-differential Barbashin equations in function spaces” [in Russian], Probl. Mat. Anal. 67, 61–68 (2012); J. Math. Sci., New York 188, No. 3, 241–249 (2013).
A. S. Kalitvin and V. A. Kalitvin, Volterra and Volterra–Fredholm Integral Equations with Partial Integrals [in Russian], Lipetsk (2006).
V. L. Levin, “Tensor products and functors in categories of Banach spaces defined by KM-lineals” [in Russian], Tr. Moskov. Mat. Ob-va 20, 43–82 (1969); English transl.: Trans. Mosc. Math. Soc. 20, 41–77 (1969).
N. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory, John Wiley & Sons, New York etc. (1988)
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Matematicheskogo Analiza 80, April 2015, pp. 11-17.
Rights and permissions
About this article
Cite this article
Kalitvin, A.S. Generalizaed Solutions to the Cauchy Problem for the Barbashin Integro-differential Equations. J Math Sci 208, 160–167 (2015). https://doi.org/10.1007/s10958-015-2433-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-015-2433-2