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)(t)+p(t)y(n)(t)+q(t)f(y(g(t)))=0 $$ y^{(n+2)}(t)+p(t)y^{(n)}(t)+q(t)f\bigl(y\bigl(g(t)\bigr)\bigr)=0 $$ 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.

Abstract licence: CC BY-NC-ND

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