Abstract
We establish conditions under which the existence of a periodic solution of a differential equation is preserved if a solution of the corresponding difference equation possesses the same property. We prove the convergence of periodic solutions of a system of difference equations to a periodic solution of a system of differential equations. Analogous problems are considered for bounded solutions.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 989–996, July, 2005.
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Stanzhyts'kyi, O.M., Tkachuk, A.M. On the Relationship between Properties of Solutions of Difference Equations and the Corresponding Differential Equations. Ukr Math J 57, 1167–1176 (2005). https://doi.org/10.1007/s11253-005-0253-0
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DOI: https://doi.org/10.1007/s11253-005-0253-0