Abstract and Applied Analysis
Volume 2010 (2010), Article ID 278962, 19 pages
doi:10.1155/2010/278962
Research Article

Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument

Miroslav Bartušek,1 Mariella Cecchi,2 Zuzana Došlá,1 and Mauro Marini2

1Department of Mathematics and Statistics, Masaryk University, CZ-61137 Brno, Czech Republic
2Department of Electronic and Telecommunications, University of Florence, I-50139 Florence, Italy

Received 21 October 2009; Accepted 5 January 2010

Academic Editor: Paul Eloe

Copyright © 2010 Miroslav Bartušek 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.

Abstract

We study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argument x‴(t)+q(t)x′(t)+r(t)f(x(φ(t)))=0. Motivated by the work of Kiguradze (1992), the existence and asymptotic properties of nonoscillatory solutions are investigated in case when the differential operator ℒx=x‴+q(t)x′ is oscillatory.