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

Abstract

We establish some new criteria for the oscillation of the even order neutral dynamic equation \begin{equation*} \left( a(t)\left( \left( x(t)-p(t)x(\tau (t))\right) ^{\Delta^{n-1}}\right) ^{\alpha }\right) ^{\Delta }+q(t)\left( x^{\sigma}(g(t))\right) ^{\lambda }=0 \end{equation*} on a time scale $\mathbb{T}$, where $n \geq 2$ is even, $\alpha $ 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 $\tau $ are real valued rd-continuous functions on $\mathbb{T}$. Examples illustrating the results are included.

Keywords

• oscillation
• neutral delay equations
• time scale
• higher order
• even order