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

Abstract

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.

Keywords

• Asymptotic behavior
• delay differential equation
• higher order differential equation
• oscillation
• Schwarz inequality