Tkachuk A. M.
Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1249–1256
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.
On the Relationship between Properties of Solutions of Difference Equations and the Corresponding Differential Equations
Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 989–996
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.