Linear attraction in quasi-linear difference systems

Abstract

The equivalence and asymptotic equivalence between the solutions of a linear difference system and some families of quasi-linear ones are studied by using a Lipschitz component-wise condition combined with a spectrally small dichotomy, which is introduced. The equivalence is described by a homeomorphism and the results also include unbounded solutions. The results show the vectorial attractivity of the solutions of the linear part.

Keywords:

• generalized Banach spaces
• component wise conditions
• dichotomy
• spectral radius
• vectorial asymptotic formulae
• difference systems

1991 Mathematics Subject Classification::

• 39A10
• 39A11

Acknowledgements

The authors are grateful for the constructive and judicious referee's comments.

Notes

1. Research supported in part by Fondecyt 1030535, 1080034 and DGI-Math Unap 2007.

2. Grant DGI Math Unap 784, 2008.

Additional information

Notes on contributors

Manuel Pinto

1

Victor Torres

2