Stability of continuous and discrete Volterra integro-differential equations by Liapunov approach
The authors extend results from the classical Lyapunov stability theory for ordinary differential equations to systems of Volterra integro-differential equations. (No reference is made to related results obtained in recent years by, for example, \textit{T. A. Burton}: Stability and periodic solutions of ordinary and functional differential equations, Academic Press, Orlando, (1985; Zbl 0635.34001).) An analogous theory is then developed for difference equations of unbounded order, and the results are illustrated by applying them to difference equations arising in the discretization of Volterra integro-differential equations by linear multistep methods. There are no examples, and it appears that (at present) this discrete theory has limited application in concrete situations.
discrete Volterra integro-differential equations
systems of Volterra integro-differential equations
scientific article; zbMATH DE number 885489