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

Oscillatory Behavior and Asymptotic Behavior of Certain Third-Order Functional Differential Equations with Distributed Delays

作为机械、电子振荡的数学模型——泛函微分方程的振动性研究在理论和实际中都有着重要意义.对于二阶泛函微分方程的振动性已经有了许多结果,但对于三阶中立型泛函微分方程的振动性研究结果却很少.利用广义Riccati变换和Hardy-Littlewood-Polya不等式,研究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,建立了该类方程的所有解振动或收敛于零的两个新的充分条件,推广和改进了一些文献中的结果.

The research on oscillation for general mechanical and electronic vibration mathematical models,which are usually functional differential equations, has important implications in both theory and practice.There have been many results about the oscillation for second order functional differential equations, but there are few research results about the third order case.By means of the generalized Riccati transformation and Hardy-Littlewood-Polya inequality, this paper establishes several new oscillation criteria for certain third order functional differential equations with distributed delays, which generalize and improve some known results in the literature.