标题： 脉冲微分方程的振荡行为通过差分方程研究具有不连续偏差变量的线性非自治超前和滞后微分方程 显示英文标题

标题： Oscillatory Behavior of Linear Nonautonomous Advanced and Delayed Impulsive Differential Equations with Discontinuous Deviating Arguments via Difference Equations

摘要： 我们建立充分条件以保证非自治的具有分段常数变量的高级和延迟线性微分方程解的振动和非振动行为：\[ x'(t) = a(t)x(t) + b(t)x([t \pm k]), \]其中$k \in \mathbb{N}$,$k \geq 1$，在脉冲和非脉冲情况下（DEPCA 和 IDEPCA）。由于这些系统的混合性质，我们的方法借鉴了高级和延迟线性差分方程理论的结果。分析涵盖了各种带有偏差变量的微分方程，其中许多已被作为特殊情况研究过。 显示英文摘要

摘要： We establish sufficient conditions to guarantee the oscillatory and non-oscillatory behavior of solutions to nonautonomous advanced and delayed linear differential equations with piecewise constant arguments: \[ x'(t) = a(t)x(t) + b(t)x([t \pm k]), \] where $k \in \mathbb{N}$, $k \geq 1$, in both impulsive and non-impulsive cases (DEPCA and IDEPCA). Due to the hybrid nature of these systems, our approach draws on results from the theory of advanced and delayed linear difference equations. The analysis encompasses various types of differential equations with deviating arguments, many of which have been previously studied as special cases.