In the present paper, we obtain a Halanay inequality on time scales with unbounded coefficient for a dynamic problem, which extends a result of Wen et al. ( J. Math. Anal. Appl. , 347 (2008), 169–178.) to the inequality of integral type on time scales. Moreover, we list two dynamic problems to which the Halanay inequality obtained above can be applied and prove the zero solution of two delay dynamic problems are asymptotically stable. Moreover, it is worth mentioning that the Halanay inequality obtained in the present paper is more precise than the results in [3, 14, 17].

中文翻译：

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具有无界系数的时标上的Halanay不等式及其应用

在本文中，我们获得了时间尺度上具有无穷大系数的动力学问题的Halanay不等式，扩展了Wen 等人的结果 。 （ J. Math。Anal。Appl 。 ， 347 （2008），169-178。）讨论时标上整数类型的不等式。此外，我们列出了上面得到的Halanay不等式可以应用的两个动力学问题，并证明了两个时滞动力学问题的零解是渐近稳定的。此外，值得一提的是，本文中获得的Halanay不等式比[3，14，17]中的结果更为精确。