Oscillation Criteria for Certain Second-Order Nonlinear Neutral Differential Equations of Mixed Type

and Applied Analysis 3 where n ≥ 1 is odd. Grace 27 and Yan 28 obtained several sufficient conditions for the oscillation of solutions of higher-order neutral functional differential equation of the form x t cx t − h Cx t H n qxt − g Qx t G 0, t ≥ t0, 1.8 where q and Q are nonnegative real constants. Clearly, 1.6 is a special case of 1.1 . The purpose of this paper is to study the oscillation behavior of 1.1 . In the sequel, when we write a functional inequality without specifying its domain of validity we assume that it holds for all sufficiently large t. 2. Main Results In the following, we give our results. Theorem 2.1. Assume that σi > τi, i 1, 2. If lim sup t→∞ ∫ t σ2−τ2 t t σ2 − τ2 − s Q2 s ds > ( 2γ−1 )2 ( 1 p 1 p γ 2 2γ−1 ) , 2.1 lim sup t→∞ ∫ t t−σ1 τ1 s − t σ1 − τ1 Q1 s ds > ( 2γ−1 )2 ( 1 p 1 p γ 2 2γ−1 ) , 2.2