Open Access

Asymptotic estimates and exponential stability for higher-order monotone difference equations

Advances in Difference Equations20052005:947201

DOI: 10.1155/ADE.2005.41

Received: 21 May 2004

Published: 14 March 2005

Abstract

Asymptotic estimates are established for higher-order scalar difference equations and inequalities the right-hand sides of which generate a monotone system with respect to the discrete exponential ordering. It is shown that in some cases the exponential estimates can be replaced with a more precise limit relation. As corollaries, a generalization of discrete Halanay-type inequalities and explicit sufficient conditions for the global exponential stability of the zero solution are given.

Authors’ Affiliations

(1)
Departamento de Matemática Aplicada II, ETSI Telecomunicación, Universidade de Vigo
(2)
Department of Mathematics and Computing, University of Veszprem

Copyright

© Hindawi Publishing Corporation 2005