一类三阶非线性中立型阻尼泛函微分方程的振动性  

Oscillation of third order nonlinear neutral differential equations with a damping term

作　　者：米雪[1] 李德生[1] 

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2016年第1期45-50,共6页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅高等学校科学研究资助项目(L2010513)

摘　　要：关于带阻尼项的中立型泛函微分方程振动性理论的研究,大多围绕着二阶微分方程进行,对于高阶微分方程讨论的较少。对一类三阶非线性中立型阻尼泛函微分方程,通过构造广义Riccati变换,并巧妙使用权函数及积分平均方法的技巧,简化了证明步骤,建立了2个新的保证此方程解振动的定理。当r1(t)=1时,该方程即为文献[13]中讨论的方程,且在证明过程中改进了文献[13]中的Riccati变换,故所得定理包含并推广了文献[13]的结果。由于该方程的一般性,所得结论不仅普遍适用于前人讨论的三阶泛函微分方程。亦为以后三阶及更高阶泛函微分方程振动性理论的研究做了铺垫。最后给出了2个具体实例来说明文章的主要结论。Most of the scholars who have studied the oscillation theory of neutral nonlinear differential equations with a damping term focus on the second order differential equations.There are a few conclusions about high order equations.This note is concerned with the oscillation of third order nonlinear neutral differential equations with a damping term.In this paper,by using ageneralized Riccati transformation technique,general weight function and integral averaging technique skillfully,we simplify the proof steps and obtain two new sufficient conditions for the oscillation of the above equation.The equation changes into the equation of [13]when r1（t）=1and we improve the generalized Riccati transformation of[13].Thus the new theorems include and improve the theorems of[13].We shall improve and unify the results given in the above mentioned papers because of the generality of equation.The results of this paper are also in preparation for the further study of oscillation of third order and higher order differential equations.Two examples are inserted to illustrate the main results.

关 键 词：振动性 三阶非线性微分方程 阻尼项 Riccati变换方法 

分 类 号：O175.10[理学—数学]