Results and problems about solutions of perturbed Lyness' type order k difference equations in , with examples, and test of the efficiency of a quasi-Lyapunov function method

Abstract

We set the problem of the convergence of every solution of the perturbed Lyness' type order k difference equation in the title, and study partly two examples: the perturbed classical order k Lyness' equation and the second-order difference equation in , , for certain domains of values for the parameters. For these two examples, we test the efficiency of a quasi-Lyapunov function method which generalizes a method introduced in a particular case by Merino.

Keywords:

• difference equations
• perturbed Lyness' type equations
• dynamical systems

2000 Mathematics Subject Classification::

• 39A20

Notes

1. [email protected]

Additional information

Notes on contributors

Guy Bastien

1