Advances in Difference Equations
Volume 2010 (2010), Article ID 693867, 12 pages
doi:10.1155/2010/693867
Research Article

Oscillation of Solutions of a Linear Second-Order Discrete-Delayed Equation

J. Baštinec,1 J. Diblík,1,2 and Z. Šmarda1

1Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech Republic
2Brno University of Technology, Brno, Czech Republic

Received 5 January 2010; Accepted 31 March 2010

Academic Editor: Leonid Berezansky

Copyright © 2010 J. Baštinec et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A linear second-order discrete-delayed equation Δx(n)=−p(n)x(n−1) with a positive coefficient p is considered for n→∞. This equation is known to have a positive solution if p fulfils an inequality. The goal of the paper is to show that, in the case of the opposite inequality for p, all solutions of the equation considered are oscillating for n→∞.