Discrete Dynamics in Nature and Society 
Volume 2004 (2004), Issue 2, Pages 301-306
doi:10.1155/S1026022604312021

Nonlinear Volterra difference equations in space lp

Michael I. Gil'1 and Rigoberto Medina2

 1Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
2Departamento de Ciencias Exactas, Universidad de Los Lagos, Osorno Casilla 933, Chile
Received 4 December 2003

Abstract

We consider a class of vector nonlinear discrete-time Volterra equations in space lp and derive estimates for the norms of solutions. These estimates give us explicit stability conditions, which allow us to avoid finding Lyapunov functionals.