On the Growth of Nonoscillatory Solutions for Difference Equations with Deviating Argument

The half-linear difference equations with the deviating argument Δ(an|Δxn|αsgn Δxn)+bn|xn+q|αsgn xn+q=0 , q ∈ ℤ are considered. We study the role of the deviating argument q, especially as regards the growth of the nonoscillatory solutions and the oscill...

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Bibliographic Details
Main Authors: M. Marini, Z. Došlá, M. Cecchi
Format: Article
Language:English
Published: SpringerOpen 2008-08-01
Series:Advances in Difference Equations
Online Access:http://dx.doi.org/10.1155/2008/505324
Description
Summary:The half-linear difference equations with the deviating argument Δ(an|Δxn|αsgn Δxn)+bn|xn+q|αsgn xn+q=0 , q ∈ ℤ are considered. We study the role of the deviating argument q, 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 (q = 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.
ISSN:1687-1839
1687-1847