Abstract
For operator differential equations in a Banach space, we present the conditions for initial data which are necessary and sufficient for the Cauchy problem to have a solution in the class of analytic, entire, or exponential-type entire vector functions. In the case where an operator differential equation is a system of partial differential equations, the sufficient condition obtained coincides with the well-known Cauchy-Kovalevskaya theorem on the solvability of the Cauchy problem in the class of analytic functions.
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Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 7–12, April–June, 1998.
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Gorbachuk, M.L. Operator approach to the Cauchy-Kovalevskaya theorem. J Math Sci 99, 1527–1532 (2000). https://doi.org/10.1007/BF02674175
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DOI: https://doi.org/10.1007/BF02674175