Abstract
Consider the neutral functional differential equation
(1) d/dt[x(t) - p(t)x(t - r)] + q(t)x(t - T(t)) = 0
where p,q,T is an element of C(R+, R+), r is an element of R+. We establish new criteria for the oscillation of all solutions of equation (1) which do not require that
(2) q(t) greater than or equal to k > 0 and 0 less than or equal to p(t) less than or equal to 1.
Our results improve some recent results in the literature.