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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 6935069, 8 pages
Research Article

Boundedness and Asymptotic Stability for the Solution of Homogeneous Volterra Discrete Equations

1Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy
2C.N.R. National Research Council of Italy, Institute for Computational Application “Mauro Picone”, Via P. Castellino 111, 80131 Napoli, Italy

Correspondence should be addressed to E. Messina; ti.aninu@anissem.aronoele

Received 17 November 2017; Revised 9 January 2018; Accepted 15 January 2018; Published 15 February 2018

Academic Editor: Mustafa R. S. Kulenovic

Copyright © 2018 E. Messina and A. Vecchio. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider homogeneous linear Volterra Discrete Equations and we study the asymptotic behaviour of their solutions under hypothesis on the sign of the coefficients and of the first- and second-order differences. The results are then used to analyse the numerical stability of some classes of Volterra integrodifferential equations.