Oscillation and Existence of Positive Solutions for Odd-Order Neutral Equations with ‘‘Integrally Small’’ Coefficients*

Consider the odd-order neutral differential equation n. wx t.yP t.x tyt.xqQ t.x tys .s0. We establish several new sufficient conditions for the oscillation of all solutions and the existence of a positive solution when P t.y1 is allowed to oscillate and the usual divergent condition H` Q s. dss` is not satisfied. These conditions are almost sharp and improve some known results in the literature. Some examples are given to demonstrate the advantage of our results.