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

Abstract

Employing a generalized Riccati transformation and integral averaging technique, we show that all solutions of the higher order nonlinear delay differential equation $y^{(n+2)}\left(t\right)+p\left(t\right)y^{\left(n\right)}\left(t\right)+q\left(t\right)f\left(y\left(g\right(t\left)\right)\right)=0$ 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.