具正负系数的二阶阻尼微分方程的振动性  

Oscillation of second order damped differential equation with positive and negative coefficients

作　　者：杨甲山[1] 张晓建[1] 

机构地区：[1]邵阳学院理学与信息科学系,湖南邵阳422004

出　　处：《高校应用数学学报（A辑）》2011年第4期399-406,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：湖南省教育厅自然科学基金(09A082);湖南省教育厅科研项目(10C1189)

摘　　要：研究了一类具有正负系数的二阶非线性变时滞中立型阻尼泛函微分方程的振动性,通过引入参数函数和Riccati变换,获得了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果,并给出了例子用以说明本文的主要结论。This paper discussed oscillation of a class of second order nonlinear variable delay neutral damped functional differential equation with positive and negative coefficients.By introducing parameter function and the generalized Riccati transformation,some criteria for the oscillation of the equation are proposed.These criteria can improve the restriction of the conditions for the equation. Some existed results in the literatures have been further improved and extended.An example is given to illustrate the main results of the paper.

关 键 词：正负系数 中立型泛函微分方程 变时滞 振动性 阻尼项 RICCATI变换 

分 类 号：O175.7[理学—数学]