三阶中立型分布时滞微分方程的振动定理  

Oscillation Theorems for Third Order Neutral Differential Equations with Distributed Delay

作　　者：仉志余[1] 王晓霞[1] 俞元洪[2] 

机构地区：[1]太原工业学院数学系,太原030008 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《工程数学学报》2013年第6期871-880,共10页Chinese Journal of Engineering Mathematics

基　　金：山西省自然科学基金(2011011002-3)~~

摘　　要：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.本文利用广义Riccati变换研究一类三阶中立型分布时滞微分方程,建立了几个新的振动准则,所得结果推广和改进了最近文献中的某些结果.The research on oscillation for general mechanical and electronic vibration mathe- matical 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 neutral functional differential equations, but there are few research results about the third order case. By means of the generalized Riccati transformation, this paper establishes several new oscillation criteria for certain third order neutral functional differential equations with distributed delays, and gives an example to illustrate the results, which generalize and improve some known results in the literature.

关 键 词：三阶中立型微分方程 振动准则 广义Riccati变换 分布时滞 

分 类 号：O175.12[理学—数学]