We investigate the Hyers—Ulam stability (HUS) of certain second-order linear constant coefficient dynamic equations on time scales, building on recent results for first-order constant coefficient time-scale equations. In particular, for the case where the roots of the characteristic equation are non-zero real numbers that are positively regressive on the time scale, we establish that the best HUS constant in this case is the reciprocal of the absolute product of these two roots. Conditions for instability are also given.

中文翻译：

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Hyers—时间尺度上二阶线性动力学方程的乌拉姆稳定性

我们研究了时间尺度上某些二阶线性常系数动态方程的 Hyers-Ulam 稳定性 (HUS)，以一阶常系数时间尺度方程的最新结果为基础。特别是，对于特征方程的根是在时间尺度上正回归的非零实数的情况，我们确定这种情况下的最佳 HUS 常数是这两个根的绝对乘积的倒数。还给出了不稳定的条件。