Oscillation criteria for third order nonlinear delay differential equations with damping

This note is concerned with the oscillation of third order nonlinear delay differential equations of the form (r_2(t) (r_q(t)y^\prime(t))^\prime)^\prime + p(t)y^\prime(t)+q(t)f(y(g(t))) = 0$. (*) In the papers [A.Tiryaki, M.F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007), 54-68] and [M.F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear-functional differential equations, Applied Math. Letters 23 (2010), 756-762], the authors established some sufficient conditions which insure that any solution of equation (*) oscillates or converges to zero, provided that the second order equation $(r_2(t)z^\prime(t))^\prime + (p(t)//r_1(t))z(t)=0$ (**) is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (*) oscillates if equation (**) is nonoscillatory. We also establish results for the oscillation of equation (*) when equation (**) is oscillatory