The paper deals with oscillation and asymptotic behaviour of the nonlinear third order equation , where are nonnegative functions and , for . Conditions on the functions are given which guarantee that no nonoscillatory solution of has property provided certain (nonlinear) second order equation associated with is oscillatory (a solution of is said to possess property if , , for large , where , , , . As a corollary of these results the following oscillation criterion is proved.
Theorem. Let any condition which implies that no nonoscillatory solution of has property be satisfied. A solution of which exists on an interval is oscillatory if and only if there exists such that for .