Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 867623, 18 pages
doi:10.1155/2008/867623
Asymptotic behavior of solutions for nonlinear Volterra discrete equations
E. Messina1
, Y. Muroya2
, E. Russo1
and A. Vecchio4
1Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
2Department of Mathematics, Waseda University, 3-4-1 Ohkubo Shinjuku-ku, Tokyo 169-8555, Japan
4Istituto per le Applicazioni del Calcolo “Mauro Picone”, Sede di Napoli, Via P. Castellino 111, 80131 Napoli, Italy
Abstract
We consider nonlinear difference equations of unbounded order of the form xi=bi−∑j=0iai,jfi−j(xj), i=0,1,2,…, where fj(x) (j=0,…,i) are suitable functions. We establish sufficient conditions for the boundedness and the convergence of xi as i→+∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.