Dissipativity of differential equations and the corresponding difference equations - Stanzhitskii, A. N.; Tkachuk, A. M. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
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.