Abstract and Applied Analysis
Volume 2012 (2012), Article ID 471435, 19 pages
http://dx.doi.org/10.1155/2012/471435
Research Article

Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients

Petr Hasil1 and Michal Veselý2

1Department of Mathematics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic
2Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

Received 28 May 2012; Revised 10 September 2012; Accepted 13 September 2012

Academic Editor: Elena Braverman

Copyright © 2012 Petr Hasil and Michal Veselý. 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

We investigate a type of the Sturm-Liouville difference equations with almost periodic coefficients. We prove that there exists a constant, which is the borderline between the oscillation and the nonoscillation of these equations. We compute this oscillation constant explicitly. If the almost periodic coefficients are replaced by constants, our result reduces to the well-known result about the discrete Euler equation.