** Authors:**
ALI MUHIB, ELMETWALLY M. ELABBASY, OSAMA MOAAZ

** Abstract: **
The aim of this article is to establish some new oscillation criteria for
the differential equation of even-order of the form
\begin{equation*}
(r\left( l\right) (y^{\left( n-1\right) }\left( l\right) )^{\alpha
})^{\prime }+f(l,x(\tau (l)))=0,
\end{equation*}
where $y\left( l\right) =x\left( l\right) +p\left( l\right) x^{\beta }\left(
\sigma _{1}\left( l\right) \right) +h\left( l\right) x^{\delta }\left(
\sigma _{2}\left( l\right) \right) $. By using Riccati transformations, we
present new conditions for oscillation of the studied equation. Furthermore,
two illustrative examples showing applicability of the new results are
included.

** Keywords: **
Sublinear and superlinear neutral terms, even-order differential
equations, oscillation criteria

** Full Text:** PDF