Dissipativity of differential equations and the corresponding difference equations
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.
English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 9, pp 1415-1424.
Citation Example: Stanzhitskii A. N., Tkachuk A. M. Dissipativity of differential equations and the corresponding difference equations // Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1249–1256.