一类时变偶阶微分方程的Philos型准则

Philos Criterion for a Class of Time-Varying Even-Order Differential Equations

振荡理论是微分方程领域的一个重要分支,在物理学和数学中起着基础性作用。尽管微分方程振荡行为的研究已经取得了许多成果,但是关于同时包含非线性中性项、阻尼项、不同符号系数和多变量延迟的非线性偶阶微分方程的研究相对较少,为此重点研究了具有上述特征的非线性偶阶微分方程的振荡行为,并得出一些相关结论。

Oscillation theory is an essential branch in the field of differential equations,playing a fundamental role both in physics and mathematics.Although there have been numerous research achievements regarding the study of oscillatory behavior in differential equations,the literature on nonlinear even-order differential equations with simultaneous inclusion of nonlinear neutral terms,damping terms,coefficients with varying signs,and multiple variable delays is relatively scarce.This paper focuses on investigating the oscillatory behavior of such nonlinear even-order differential equations with the mentioned characteristics,and presents several relevant conclusions.