Abstract
We establish conditions under which the existence of a bounded solution of a difference equation yields the existence of a bounded solution of the corresponding differential equation. We investigate the relationship between the dissipativities of differential and difference equations in terms of Lyapunov functions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1249–1256, September, 2006.
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Stanzhyts’kyi, O.M., Tkachuk, A.M. Dissipativity of differential equations and the corresponding difference equations. Ukr Math J 58, 1415–1424 (2006). https://doi.org/10.1007/s11253-006-0140-3
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DOI: https://doi.org/10.1007/s11253-006-0140-3