An oscillation criterion for first order linear delay differential equations

A new oscillation criterion is given for the delay differential equation x'(t) + p(t)x (t - tau(t)) = 0, where p, tau is an element of ([0, infinity), [0, infinity)) and the function T defined by T(t) = t - tau(t), t greater than or equal to 0 is increasing and such that lim(t-->infinity) T(t) = infinity. This criterion concerns the case where lim inf(t-->infinity) integral(T(t))(t )p(s) ds less than or equal to 1/e.