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arXiv · 2012.10726

Stability and oscillation of linear delay differential equations

John Ioannis Stavroulakis·Elena Braverman
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Abstract

There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of any sign, $\tau(t)\leq t$ is Lebesgue measurable, $\lim_{t\rightarrow\infty}\tau(t)=\infty$, we obtain sharp results, relating the speed of oscillation and stability. We thus unify the classical results of Myshkis and Lillo. We also generalise the $3/2-$stability criterion to the case of measurable parameters, improving $1+1/e$ to the sharp $3/2$ constant.

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John Ioannis Stavroulakis, Elena Braverman. 2020-12-19. Stability and oscillation of linear delay differential equations. https://doi.org/10.1016/j.jde.2021.05.021

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