Advances in Difference Equations
Volume 2008 (2008), Article ID 505324, 15 pages
On the Growth of Nonoscillatory Solutions for Difference Equations
with Deviating Argument
1Department of Electronics and Telecommunications, University of Florence, Via S. Marta 3, 50139 Firenze, Italy
2Department of Mathematics and Statistics, Masaryk University, Janáčkovo nám. 2a, 60200 Brno, Czech Republic
Received 28 March 2008; Accepted 27 May 2008
Academic Editor: Martin Bohner
Copyright © 2008 M. Cecchi 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.
The half-linear difference equations with the deviating argument
are considered. We study the role of the deviating argument
, especially as regards
the growth of the nonoscillatory solutions and the oscillation.
Moreover, the problem of the existence of the intermediate solutions is completely
resolved for the classical half-linear equation ( = 1). Some analogies
or discrepancies on the growth of the nonoscillatory solutions for the delayed
and advanced equations are presented; and the coexistence with different types
of nonoscillatory solutions is studied.