About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 432936, 12 pages
http://dx.doi.org/10.1155/2013/432936
Research Article

Oscillation and Nonoscillation of Asymptotically Almost Periodic Half-Linear Difference Equations

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

Received 18 March 2013; Accepted 20 May 2013

Academic Editor: Ondrej Dosly

Copyright © 2013 Michal Veselý and Petr Hasil. 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 analyse half-linear difference equations with asymptotically almost periodic coefficients. Using the adapted Riccati transformation, we prove that these equations are conditionally oscillatory. We explicitly find a constant, determined by the coefficients of a given equation, which is the borderline between the oscillation and the nonoscillation of the equation. We also mention corollaries of our result with several examples.