论文标题
线性延迟微分方程的稳定性和振荡
Stability and oscillation of linear delay differential equations
论文作者
论文摘要
稳定性和延迟微分方程的振荡之间存在密切的联系。对于一阶方程$$ x^{\ prime}（t）+c（t）+c（t）x（τ（t））= 0，~~ t \ geq 0，$ c $ $ c $在任何标志上都可以在任何标志上集成，$τ（t）\ leq t $是lebesgue，lebesgue是lebesgue，lebesgue，lebesgue，$ \ \ fim_ flem_ fery $ \ \ fery we \ right \ right \ fery we \ fery we \ ferty unfty，与振荡和稳定性的速度有关。因此，我们统一了Myshkis和Lillo的经典结果。我们还将$ 3/2- $稳定性标准推广到可衡量参数的情况下，将$ 1+1/e $提高到夏普$ 3/2 $常数。
There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(τ(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of any sign, $τ(t)\leq t$ is Lebesgue measurable, $\lim_{t\rightarrow\infty}τ(t)=\infty$, 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.
