Oscillation theorems for higher order neutral nonlinear dynamic equations on time scales

A. Benaissa Cherif a,* F. Z. Ladranib and A. Hammoudia

Oscillation theorems for higher order neutral nonlinear dynamic equations on time scales

Authors :

A. Benaissa Cherif ^a,* F. Z. Ladrani^b and A. Hammoudi^a

Author Address :

^aDepartment of Mathematics, University of Ain Temouchent, BP 284, 46000 Ain Temouchent, Algeria.
^bDepartment of Mathematics, Higher normal school of Oran, BP 1523, 31000 Oran, Algeria.

*Corresponding author.

Abstract :

In this paper, we will establish some oscillation criteria for the even-order nonlinear dynamic equation
\begin{equation*}
\left( a\left( x^{\Delta ^{n-2}}\right) ^{\gamma }\right) ^{\Delta
^{2}}\left( t\right) +f\left( t,x^{\alpha }\left( t\right) \right) =0,\text{%
\qquad }t\in \left[ t_{0},\infty \right) _{\mathbb{T}}
\end{equation*}%
on a time scales $\mathbb{T}$ with $n$ is an even integer $\geq 3,$ where $% \gamma $ and $\alpha $ are the ratios of positive odd integer and $a$ is areal valued rd-continuous function defined on $\mathbb{T}$.