A classification of nonoscillatory
solutions according to the sign properties of their derivatives i6 introduced for a
general nonlinear delay differential equation of order 2n. It is seen that there
are n types of positive solutions of this equation. An intermediate Riccatti
transformation is employed to obtain integral criteria for the nonexistence of
such solutions and for the oscillation of all solutions. Analysis of the Taylor
Remainder gives rise to a summability condition which is used to investigate the
asymptotic behavior of a class of solutions. The major results are then shown
to be special cases of a more general result based on the direct method of
Lyapunov.