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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 764351, 12 pages
Research Article

Asymptotic Upper and Lower Estimates of a Class of Positive Solutions of a Discrete Linear Equation with a Single Delay

1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech Republic
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech Republic

Received 20 February 2012; Accepted 1 March 2012

Academic Editor: Elena Braverman

Copyright © 2012 J. Diblík and I. Hlavičková. 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.


We study a frequently investigated class of linear difference equations with a positive coefficient and a single delay k. Recently, it was proved that if the function is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the function is bounded above and below by certain functions.