Abstract
Existence, uniqueness and continuous dependence of solutions on initial conditions theorems are proved for the Hale functional differential equations in a Banach space. Concrete examples of the use of the obtained theorems are given.
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G. E. Ladas and V. Lakshmikantham, Differential Equations in Abstract Spaces, Academic Press, New York (1972).
M. Kwapisz, “Existence and uniqueness of solutions of differential equations with deviating argument in a Banach space,” in: Proceedings of the Seminar on the Theory of Differential Equations with Deviating Argument [in Russian],6, 96–110 (1967).
B. N. Sadosvskii, “Asymptotically compact and densifying operators,” Usp. Mat. Nauk,27, No. 1, 81–146 (1972).
D. G. Korenevskii, “The abstract Cauchy problem for differential equations with deviating argument,” in: Nonlinear Oscillations and Stability of Motion [in Russian], Inst. Mat. Akad. Nauk UkrSSR, Kiev (1973), pp. 55–58.
M. Kwapisz, “On the existence and uniqueness of solutions to a certain integro-differential equation,” Ann. Pol. Mat.,31, No. 1, 23–41 (1975).
P. Hartman, Ordinary Differential Equations, S. M. Hartman, MD (1973).
M. A. Krasnosel'skii and S. G. Krein, “The theory of ordinary differential equations in Banach spaces,” Tr. Sem. Funkts. Anal., No. 2, 3–23 (1956).
J. Hale, Theory of Functional Differential Equations [Russian translation], Mir, Moscow (1984).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 918–924, July, 1990.
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Ilolov, M. Hale functional differential equations in a Banach space. Ukr Math J 42, 814–819 (1990). https://doi.org/10.1007/BF01062084
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DOI: https://doi.org/10.1007/BF01062084