On the Relationship between Properties of Solutions of Difference Equations and the Corresponding Differential Equations
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.
English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 7, pp 1167-1176.
Citation Example: Stanzhitskii A. N., Tkachuk A. M. On the Relationship between Properties of Solutions of Difference Equations and the Corresponding Differential Equations // Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 989–996.