On Oscillation Criteria for Third Order Nonlinear Delay Differential Equations

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

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


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.