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