On the oscillatory behavior of even order neutral delay dynamic equations on time-scales

摘要

We establish some new criteria for the oscillation of the even order neutral dynamic equation egin{equation*} left( a(t)left( left( x(t)-p(t)x(au (t))ight) ^{Delta^{n-1}}ight) ^{lpha }ight) ^{Delta }+q(t)left( x^{sigma}(g(t))ight) ^{lambda }=0 end{equation*} on a time scale $mathbb{T}$, where $n geq 2$ is even, $lpha $ and $lambda $ are ratios of odd positive integers, $a$, $p$ and $q$ are real valued positive rd-continuous functions defined on $mathbb{T}$, and $g$ and $au $ are real valued rd-continuous functions on $mathbb{T}$. Examples illustrating the results are included.