# On Oscillation Criteria for Third Order Nonlinear Delay Differential Equations

## Ravi P. Agarwal, Mustafa F. Aktas, and A. Tiryaki

Address:

Department of Mathematical Sciences Florida Institute of Technology Melbourne, FL 32901, USA

Department of Mathematics, Gazi University Faculty of Arts and Sciences Teknik- okullar, 06500 Ankara, Turkey

Department of Mathematics and Computer Sciences Izmir University, Faculty of Arts and Sciences 35350 Uckuyular, Izmir, Turkey

E-mail:

agarwal@fit.edu

mfahri@gazi.edu.tr

aydin.tiryaki@izmir.edu.tr

Abstract: In this paper we are concerned with the oscillation of third order nonlinear delay differential equations of the form
\[ \ \left( r_{2}\left( t\right) \left( r_{1}\left( t\right) x^{\prime }\right) ^{\prime }\right) ^{\prime }+p\left( t\right) x^{\prime }+q\left( t\right) f\left( x\left( g\left( t\right) \right) \right) =0. \]
We establish some new sufficient conditions which insure that every solution of this equation either oscillates or converges to zero.

AMSclassification: primary 34K11; secondary 34C10.

Keywords: oscillation, third order, functional differential equation.