On oscillation criteria for third order nonlinear delay differential equations

summary: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