OSCILLATION AND EXISTENCE OF POSITIVE SOLUTIONS IN A CLASS OF HIGHER-ORDER NEUTRAL EQUATIONS

Consider the higher order neutral differential equation [x(t) - x(t - tau)]((n)) + Q(t)x(t - sigma) = 0, t greater than or equal to t(0) wit h Q(t) continuous, tau > 0, sigma greater than or equal to 0, and n od d. We establish several new sufficient conditions for the oscillation of all solutions and the existence of a positive solution by an associ ated ordinary differential equation. Some of these conditions are shar p and improve the known results in the literature which include the ne west one by J. S. Yu (Chinese Ann. Math. Ser: A 16, 1995, 33-42). (C) 1997 Academic Press.