OSCILLATION OF THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Abstract

In this paper, we study the oscillatory behavior of a class of third-order nonlinear delay differential equations $$ (a(t) (b(t) y'(t))')' + q(t) y^\gamma(\tau(t)) = 0. $$ Some new oscillation criteria are presented by transforming this equation to the first-order delayed and advanced differential equations. Employing suitable comparison theorems we establish new results on oscillation of the studied equation. Assumptions in our theorems are less restrictive, these criteria improve those in the recent paper [Appl. Math. Comput., 202 (2008), 102-112] and related contributions to the subject. Examples are provided to illustrate new results.