Oscillatory solutions for dynamic equations with non-monotone arguments
Abstract
Consider the first-order delay dynamic equation
$$
x^{\Delta }(t)+p(t)x\left( \tau (t)\right) =0,\text{ }t\in [t_{0},\infty )_{\mathbb{T}}
$$
where $p\in C_{rd}\left( [t_{0},\infty )_{\mathbb{T}},\mathbb{R}^{+}\right) $, $\tau \in C_{rd}\left( [t_{0},\infty )_{\mathbb{T}},\mathbb{T}\right) $ is non-monotone, and $\tau (t)\leq t$ $,\ \lim_{t\rightarrow \infty }\tau(t)=\infty $. Under the assumption that the $\tau $ is non-monotone, we present sufficient conditions for the oscillation of first-order delay dynamic equations on time scales. An example illustrating the result is also given.Copyright © 2017 Özkan Öcalan, Umut Mutlu Ozkan, Mustafa Kemal Yildiz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
Ö. Öcalan, U. M. Ozkan, M. K. Yildiz, Oscillatory solutions for dynamic equations with non-monotone arguments, J. Math. Comput. Sci. 7 (2017), 725–738.
BibTeX
@article{Öcalan2017,
author = {Öcalan, Özkan and Ozkan, Umut Mutlu and Yildiz, Mustafa Kemal},
title = {Oscillatory solutions for dynamic equations with non-monotone arguments},
journal = {J. Math. Comput. Sci.},
volume = {7},
year = {2017},
pages = {725--738},
doi = {}
}