We study the solvability conditions for the Cauchy problem for the Barbashin integro-differential equation in the space of bounded continuous functions and in the space of continuous vector-valued functions with the values in an ideal Banach space. We also consider conditions guaranteeing the existence of classical and generalized solutions to the Cauchy problem for systems of linear Barbashin integro-differential equations. Bibliography: 5 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. N. Kolmogorov, Probability Theory and Mathematical Statistics [in Russian], Nauka, Moscow (1986); English transl.: Kluwer Acad. Publ., Dordrecht (1992).
A. S. Kalitvin, Linear Operators with Partial Integrals [in Russian], Voronezh Univ. Press, Voronezh (2000).
E. Hille and R. S. Phillips, Functional Analysis and Semigroups Am. Math. Soc., Providence, RI (1957).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Matematicheskogo Analiza 67, November 2012, pp. 61–68.
Rights and permissions
About this article
Cite this article
Kalitvin, A.S. Some aspects of the theory of integro-differential Barbashin equations in function spaces. J Math Sci 188, 241–249 (2013). https://doi.org/10.1007/s10958-012-1122-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-012-1122-7