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(1)(t)y'(t))')' + p(t)y'(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'(t))' + (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.