A new view of the lp-theory for a system of higher order difference equations

Authors:
I. Gyri;L. Horváth
Affiliations:
Department of Mathematics, University of Pannonia, Egyetem u. 10. 8200 Veszprém, Hungary;Department of Mathematics, University of Pannonia, Egyetem u. 10. 8200 Veszprém, Hungary
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

It is proved under appropriate assumptions that the solutions of a linear system of higher order difference equations belong to l^p, that is the pth powers of the solutions are summable for some p=1. Our results are based on a new transformation of the higher order system into a first-step recursion, where the companion matrices are well treatable from our point of view. Our theory is illustrated by examples, including an interesting exponential stability result and a class of linear delay difference equations.