Oscillation Test for Linear Delay Differential Equation with Nonmonotone Argument

Authors : Nurten KILIÇ

Pages : 310-317

Doi:10.47000/tjmcs.893395

View : 8 | Download : 4

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :In this article, we analyze the first order linear delay differential equation \begin{equation*} x^{\prime }insert ignore into journalissuearticles values(t);+pinsert ignore into journalissuearticles values(t);x\leftinsert ignore into journalissuearticles values( \tau insert ignore into journalissuearticles values(t);\right); =0,\text{ }t\geq t_{0}, \end{equation*} where $p,$ $\tau \in C\leftinsert ignore into journalissuearticles values( [t_{0},\infty );,\mathbb{R}^{+}\right); $ and $% \tau insert ignore into journalissuearticles values(t);\leq t,\ \lim_{t\rightarrow \infty }\tau insert ignore into journalissuearticles values(t);=\infty $. Under the assumption that $\tau insert ignore into journalissuearticles values(t);$ is not necessarily monotone, we obtain new sufficient criterion for the oscillatory solutions of this equation. We also give an example illustrating the result.
Keywords : Delay equation, nonmonotone argument, oscillatory solution, nonoscillatory solution