Asymptotic dichotomy in a class of higher order nonlinear delay differential equations.

Employing a generalized Riccati transformation and integral averaging technique, we show that all solutions of the higher order nonlinear delay differential equation y ( n + 2 ) ( t ) + p ( t ) y ( n ) ( t ) + q ( t ) f ( y ( g ( t ) ) ) = 0 will converge to zero or oscillate, under some conditions listed in the theorems of the present paper. Several examples are also given to illustrate the applications of these results.