On the Relationship between Properties of Solutions of Difference Equations and the Corresponding Differential Equations - Stanzhitskii, A. N.; Tkachuk, A. M. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
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.