Advances in Difference Equations 
Volume 2005 (2005), Issue 1, Pages 41-55
doi:10.1155/ADE.2005.41

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

Eduardo Liz1 and Mihály Pituk2

 1Departamento de Matemática Aplicada II, ETSI Telecomunicación, Universidade de Vigo, Campus Marcosende, Vigo 36280, Spain
2Department of Mathematics and Computing, University of Veszprem, P.O. Box 158, Veszprem 8201, Hungary
Received 21 May 2004

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.