一类具阻尼项的三阶非线性中立型泛函微分方程的振动性

摘要

The research on oscillation for general mechanical and electronic vibration mathematical mod-els,which are usually functional differential equations,has important implications in both theory and practice.The oscillation of third-order nonlinear neutral functional differential equations with continuous distributed delay and damping terms is studied.By using the generalized Riccati transformation,H-func-tion and integral averaging technique,some new sufficient conditions which insure that any solution of such equation oscillates or converges to zero are established.The corresponding known results are extend-ed and improved.%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。研究一类具连续分布滞量和阻尼项的三阶非线性中立型泛函微分方程的振动性，利用广义Riccati变换、H函数和积分平均技巧，建立了保证该类方程的所有解振动或收敛于零的若干新的充分条件，推广和改进了最近文献的结果。