Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations

الملخص EN

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.