Oscillatory behavior of a hyperbolic delay partial dynamic equation with time and spatial variables defined on arbitrary time scales is studied in this article. The Green’s identity on an arbitrary time scale is presented. Using that identity and Riccati transformation, several oscillation criteria for the concern dynamic equation with Neumann boundary condition is established. Examples are provided to illustrate our results.

中文翻译：

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在任意时间尺度上具有时间和空间变量的双曲时滞动力方程解的振动准则

本文研究了在任意时标上定义了时间和空间变量的双曲时滞局部动力方程的振动性。呈现了任意时间尺度上的格林身份。利用该恒等式和Riccati变换，建立了具有诺伊曼边界条件的关注动力学方程的几个振动准则。提供示例来说明我们的结果。