Abstract and Applied Analysis
Volume 2010 (2010), Article ID 278962, 19 pages
doi:10.1155/2010/278962
Oscillation for third-order nonlinear differential equations with deviating argument
Miroslav Bartušek1
, Mariella Cecchi2
, Zuzana Došlá1
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
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.