Abstract
We investigate the problem of approximation of a bounded solution of a difference analog of the differential equation
by solutions of the corresponding boundary-value problems. Here, A is an unbounded operator in a Banach space B, {A 1,...,A m-1} ⊂L(B) and f:ℝ→B is a fixed function.
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References
M. F. Gorodnii, “Bounded and periodic solutions of one difference equation and its stochastic analog in a Banach space,” Ukr. Mat. Zh., 43, No. 1, 41–46 (1991).
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).
N. Dunford and J. T. Schwartz, Linear Operators, Part 1: General Theory, Interscience, New York 1958.
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Gorodnii, M.F., Romanenko, V.M. Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems. Ukr Math J 52, 628–632 (2000). https://doi.org/10.1007/BF02515403
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DOI: https://doi.org/10.1007/BF02515403