Oscillation theorems for advanced differential equations

Amin Benaissa Cherif  ; Moussa Fethallah ; Fatima Zohra Ladrani

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

Résumé

In this paper, we will establish some oscillation criteria for the advanced differential equations \begin{equation*} u^{^{\prime }}\left( t\right) -\sum\nolimits_{i=1}^{i=k}q_{i}\left( t\right) u^{\alpha }\left( \tau _{i}\left( t\right) \right) =0\text{,\quad for }t\geq t_{0} \end{equation*}% where $k$ is an integer and $\alpha $ is a quotient of odd integers, such as $k\geq 1$ and $\alpha \geq 1$. The functions $\left\{ q_{i}\right\} _{i\in \left\{ 1,...,k\right\} }$ are continuous positive functions and the arguments $\left\{ \tau _{i}\right\} _{i\in \left\{ 1,...,k\right\} }$ are continuous positive functions, such that $\tau _{i}\left( t\right) >t$, for $% i\in \left\{ 1,...,k\right\} $. This study aims to present some new sufficient conditions for the oscillation of solutions to a class of first-order advanced differential equations, using a technique based on a recursive sequence.

Détail

Publié le : 2022-01-27

DOI : 10.30755/NSJOM.12180

Classification : 34K06, 34K11
Keywords: oscillation, advanced differential equations