Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. The purpose of this article is to explore the oscillation of fourth-order differential equations with delay arguments. New Kamenev-type oscillatory properties are established, which are based on a suitable Riccati method to reduce the main equation into a first-order inequality. Our new results extend and simplify existing results in the previous studies. Examples are presented in order to clarify the main results.

中文翻译：

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微分方程解的振动性中的对称性及其重要性

振动和对称性在许多应用中起着重要作用，例如工程，物理，医学和飞行中的振动。本文的目的是探讨带时滞参数的四阶微分方程的振动性。建立了新的Kamenev型振动特性，其基于合适的Riccati方法将主方程式简化为一阶不等式。我们的新结果扩展并简化了先前研究中的现有结果。给出示例以阐明主要结果。