  We obtain several new comparison results on the distance between zeros and
local extrema of solutions for the second order delay differential equation
\begin{equation*} x^{\prime \prime }(t)+p(t)x(t-\tau (t))=0,~~t\geq s\text{ }\
\end{equation*} where $\tau :\mathbb{R}\rightarrow \lbrack 0,+\infty )$,
$p:\mathbb{R}% \rightarrow \mathbb{R}$ are Lebesgue measurable and uniformly
essentially bounded, including the case of a sign-changing coefficient. We are
thus able to calculate upper bounds on the semicycle length, which guarantee
that an oscillatory solution is bounded or even tends to zero. Using the
estimates of the distance between zeros and extrema, we investigate the
classification of solutions in the case $p(t)\leq 0,t\in \mathbb{R}.$
