一类具分布时滞的三阶非线性泛函微分方程的振动性和渐近性

Oscillation and Asymptotic Behavior of a Class of Third Order Nonlinear Functional Differential Equations with Distributed Delays

在本文中,我们重点研究几个泛函微分方程的振动和渐近行为。本文还研究了三阶非线性中立分布时滞微分方程的振动和三阶非线性中立型多分布时滞微分方程的振动。我们使用一般Riccati和对称不等式,来测试非线性第三线性泛函微分方程的振动和渐近行为。设定了解决振动或聚焦零方程的两个新的富集条件。在研究过程中,创建了两个方程的几个新解的振动的充实要求,并使用算子和积分模式实行了恰当的对比定理。由此产生的定理扩张并优化了现有的结果,也适用于中性微分方程。

In this paper,we focus on the oscillation and asymptotic behavior of several functional differential equations.In this paper,the oscillations of third-order nonlinear neutral distributed delay differential equations and third-order nonlinear neutral multi-distributed delay differential equations are also studied.We use general Riccati and symmetric inequalities to test the oscillation and asymptotic behavior of nonlinear third linear functional differential equations.Two new enrichment conditions are set up to solve the zero equation of vibration or focusing.In the course of the study,the sufficient requirements for the oscillation of several new solutions of the two equations are created,and the appropriate comparison theorem is implemented by using operators and integral modes.The resulting theorem extends and optimizes the existing results and is also applicable to neutral differential equations.