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.
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J. M. Appell, A. S. Kalitvin, and P. P. Zabrejko, Partial Integral Operators and Integro-Differential Equations, Marcel Dekker, New York (2000).
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Translated from Problemy Matematicheskogo Analiza 67, November 2012, pp. 61–68.
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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
- Banach Space
- Generalize Solution
- Cauchy Problem
- Measurable Function
- Integral Operator