- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 2
- Oscillation criteria for first-order dynamic equations with nonmonotone delays
Oscillation criteria for first-order dynamic equations with nonmonotone delays
Authors : Nurten Kiliç, Özkan Öcalan
Pages : 318-325
Doi:10.15672/hujms.674428
View : 12 | Download : 6
Publication Date : 2021-04-11
Article Type : Research
Abstract : In this paper, we consider the first-order dynamic equation as the following: $$x^{\Delta}(t)+\sum\limits_{i=1}^m p_i(t)x(\tau_i(t))=0,\,\,t\in[t_0,\infty)_{\mathbb{T}}$$ where $p_{i}\in C_{rd}\left( [t_{0},\infty )_{\mathbb{T}},\mathbb{R}^{+}\right) ,$ $\tau _{i}\in C_{rd}\left( [t_{0},\infty )_{\mathbb{T}},\mathbb{T}\right) $ $(i=1,2,\ldots ,m)$ and $\tau_i(t)\leq t,\,\, \lim_{t\to\infty}\tau_i(t)=\infty$. When the delay terms $\tau_{i}(t)$ $(i=1,2,\ldots ,m)$ are not necessarily monotone, we present new sufficient conditions for the oscillation of first-order delay dynamic equations on time scales.Keywords : dynamic equations, nonmonotone delay, oscillation, time scales