Neutral delay differential equations: An improved approach and its
applications in the oscillation theory
Abstract
The objective of this study is to establish new sufficient criteria for
the oscillation of the 2nd-order neutral equation
$\left( r\left(
z^{\prime }\right)
^{\alpha }\right)
^{\prime }\left(
t\right) +q\left( t\right)
x^{\beta }\left(
\sigma \left( t\right)
\right) =0,$ where $t\geq t_{0}$ and
$z\left( t\right) =x\left(
t\right) +px\left( \tau
\left( t\right) \right)
$%. We improve the known criteria by establishing a new relationship
between the solution $x$ and the corresponding function $z$. To show
the importance of our results, we provide two examples.