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Search: All articles in the CMB digital archive with keyword Delay differential equation

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1. CMB 2016 (vol 59 pp. 849)

Nah, Kyeongah; Röst, Gergely
Stability Threshold for Scalar Linear Periodic Delay Differential Equations
We prove that for the linear scalar delay differential equation $$ \dot{x}(t) = - a(t)x(t) + b(t)x(t-1) $$ with non-negative periodic coefficients of period $P\gt 0$, the stability threshold for the trivial solution is $r:=\int_{0}^{P} \left(b(t)-a(t) \right)\mathrm{d}t=0,$ assuming that $b(t+1)-a(t)$ does not change its sign. By constructing a class of explicit examples, we show the counter-intuitive result that in general, $r=0$ is not a stability threshold.

Keywords:delay differential equation, stability, periodic system
Categories:34K20, 34K06

2. CMB 1998 (vol 41 pp. 207)

Philos, Ch. G.; Sficas, Y. G.
An oscillation criterion for first order linear delay differential equations
A new oscillation criterion is given for the delay differential equation $x'(t)+p(t)x \left(t-\tau(t)\right)=0$, where $p$, $\tau \in \C \left([0,\infty),[0,\infty)\right)$ and the function $T$ defined by $T(t)=t-\tau(t)$, $t\ge 0$ is increasing and such that $\lim_{t\to\infty}T(t)=\infty$. This criterion concerns the case where $\liminf_{t\to\infty} \int_{T(t)}^{t}p(s)\,ds\le \frac{1}{e}$.

Keywords:Delay differential equation, oscillation

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