Browsing by Subject "delay differential equations"

Now showing 1 - 2 of 2

Access status: Open Access ,
New oscillation constraints for even-order delay differential equations
(Wydawnictwa AGH, 2023) Moaaz, Osama; Anis, Mona; El-Deeb, Ahmed A.; Elshenhab, Ahmed M.
The purpose of this paper is to study the oscillatory properties of solutions to a class of delay differential equations of even order. We focus on criteria that exclude decreasing positive solutions. As in this paper, this type of solution emerges when considering the noncanonical case of even equations. By finding a better estimate of the ratio between the Kneser solution with and without delay, we obtain new constraints that ensure that all solutions to the considered equation oscillate. The new findings improve some previous findings in the literature.
Access status: Open Access ,
Stability switches in a linear differential equation with two delays
(Wydawnictwa AGH, 2022) Hata, Yuki; Matsunaga, Hideaki
This paper is devoted to the study of the effect of delays on the asymptotic stability of a linear differential equation with two delays $x'(t)=-ax(t)-bx(t-\tau)-cx(t-2\tau),\quad t\geq 0,$ where $a$, $b$, and $c$ are real numbers and $\tau \gt 0$. We establish some explicit conditions for the zero solution of the equation to be asymptotically stable. As a corollary, it is shown that the zero solution becomes unstable eventually after undergoing stability switches finite times when $\tau$ increases only if $c-a\lt 0$ and $\sqrt{-8c(c-a)}\lt |b| \lt a+c$. The explicit stability dependence on the changing $\tau$ is also described.