Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations. (7th May 2008)

• Record Type: Journal Article
• Authors: Messina, E.; Muroya, Y.; Russo, E.; Vecchio, A.
• Other Names: Matsumoto A. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2008(2008)
• Publication Date: 2008-05-07
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2008/867623
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We consider nonlinear difference equations of unbounded order of the formx i = b i − ∑ j = 0 i a i, j f i − j ( x j ), i = 0, 1, 2, …, wheref j ( x ) ( j = 0, …, i ) are suitable functions. We establish sufficient conditions for the boundedness and the convergence ofx i asi → + ∞ . Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.