Oscillation theorems for higher order nonlinear functional dynamic equations with unbounded neutral coefficients on time scales

Abderrahmane Beniani ; Amin Benaissa Cherif  ; Fatima Zohra Ladrani ; Khaled Zennir

Novi Sad Journal of Mathematics, Tome 53 (2023) no. 2.

Résumé

In this paper, we will establish some oscillation criteria for the even-order nonlinear functional dynamic equations with unbounded neutral coefficients on time scales% \begin{equation*} \left( r(t)\left( v^{\Delta ^{n-1}}\left( t\right) \right) ^{\beta }\right) ^{\Delta }+f\left( t,\left( u\circ h\right) \left( t\right) \right) =0,\quad \text{for all }J_{t_{0}}, \end{equation*}% on a time scale $\mathbb{T}$, with $\sup \mathbb{T=\infty }$, where $\beta $ is a quotient of odd integer, such as $\beta >0$, with $J_{t_{0}}=[t_{0},% \infty )\cap \mathbb{T}$, and \begin{equation*} v(t):=u(t)+\sum\nolimits_{i=1}^{i=k}p_{i}(t)\left( u\circ \eta _{i}\right) (t),\quad \text{for all }J_{t_{0}}, \end{equation*}% where $n$ is an integer, such as $n\geq 1$. This study aims to present some new sufficient conditions for the oscillatory of solutions to a class of even-order nonlinear functional dynamic equations.

Détail

Publié le : 2022-07-20

DOI : 10.30755/NSJOM.11387

Classification : 34C10, 34C15, 34K11
Keywords: neutral differential equation, oscillation, second order time scales