Asymptotic properties of third-order nonlinear differential equations

Abstract

We present  new  criteria for all nonoscillatory solutions of  the third-order  functional differential equation

\begin{equation*}
\left[r(t)\left[x'(t)\right]^{\gamma}\right]'' +p(t) x^{\beta}(\tau(t))=0
\end{equation*}

tend to zero. Our results are based on the suitable comparison theorems. We consider both  delay and advanced case of studied equation. The results obtained
essentially improve and complement earlier ones.