Stability for planar linear discrete Hamiltonian systems with perturbations

Abstract

In this article, we will give several conditions under which the following planar linear discrete Hamiltonian system with perturbations

has the same stability as the corresponding linear system

Moreover, these conditions are shown to be necessary and sharp by examples.

Keywords:

• planar linear discrete Hamiltonian system
• perturbations
• stability
• boundedness

AMS Subject Classifications::

• 34D20
• 34E10

Acknowledgements

This work is partially supported by the NNSF (No: 11171351) of China and by Hunan Provincial Natural Science Foundation of China (No. 11JJ2005).