We consider explicit sufficient conditions for all solutions of a first-order linear difference equation with several variable delays and non-negative coefficients to be oscillatory. The conditions have the form of inequalities bounding below the upper and lower limits of the sums of coefficients over a subset of the discrete semiaxis. Our main results are oscillation tests based on a new principle for composing the estimated sums of coefficients. We also give some results in the form of examples, including a counterexample to a wrong oscillation test cited in several recent papers.

中文翻译：

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带有多个时滞的差分方程的清晰显式振动条件

我们认为具有几个可变延迟和非负系数的一阶线性差分方程的所有解的显式充分条件是振荡的。条件具有不等式的形式，该不等式限制在离散半轴的子集上的系数之和的上限和下限以下。我们的主要结果是基于一种新原理的振荡测试，该原理用于组成系数的估计和。我们还以示例的形式给出了一些结果，包括最近几篇论文中引用的错误振荡测试的反例。