Abstract
We investigate the problem of approximation of a bounded solution of a linear differential equation by solutions of the corresponding difference equations in a Banach space.
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References
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).
M. F. Gorodnii, “Bounded and periodic solutions of a difference equation and its stochastic analog in a Banach space,” Ukr. Mat. Zh., 43, No. 1, 41–46 (1991).
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M. F. Gorodnii, “Approximation of a bounded solution of one difference equation by solutions of the corresponding boundary-value problems in a Banach space,” Mat. Zametki, 51, No. 4, 17–22 (1992).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1268–1271, September, 1998.
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Gorodnii, M.F. On the approximation of a bounded solution of a linear differential equation in a Banach space. Ukr Math J 50, 1449–1453 (1998). https://doi.org/10.1007/BF02525251
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DOI: https://doi.org/10.1007/BF02525251