Oscillation theorems for second order advanced neutral differential equations

Abstract

The aim of this paper is to study the oscillation
 of the second order advanced neutral
differential
equations%
\begin{equation*}
\left(r(t)\left[x(t)+p(t)x(\tau(t))\right]'\right)'+q(t)x(\sigma(t))=0.  \tag{$E$}
\end{equation*}%
Obtained results are based on the new comparison theorems, that
enable us to reduce problem of the oscillation of the second order
equation to the the oscillation of the first order equations.
Obtained comparison principles essentially simplify the
examination of the studied equations.