一类具正负系数的二阶中立型方程的振动性  

Oscillation of a class of second order neutral differential equations with positive and negative coefficients

作　　者：杨甲山[1] 王瑀[2] 

机构地区：[1]邵阳学院理学与信息科学系,湖南邵阳422004 [2]安徽大学数学科学学院,安徽合肥230039

出　　处：《合肥工业大学学报（自然科学版）》2012年第4期552-556,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11071222);湖南省教育厅科研基金资助项目(10C1189)

摘　　要：文章研究了一类具有正负系数和变时滞的二阶非线性中立型泛函微分方程的振动性,通过引入参数函数和Riccati变换,结合Banach空间的不动点原理,获得了该类方程振动及非振动的判别准则,这些准则改善了对方程的条件限制,所得结果推广并改进了现有文献中的一系列结论。The oscillation of a class of second order nonlinear neutral functional differential equations with positiye and negative coefficients and variable delay is discussed in this paper. By introducing the parameter function and the generalized Riccati transformation, and using the fixed point theorem in Banach space, some sufficient conditions for oscillation and nonoscillation of the equations are pro- posed. These criteria can improve the restriction of the conditions for the equations. These results im- prove and generalize some corresponding results given in literature.

关 键 词：正负系数 变时滞 振动和非振动 RICCATI变换 

分 类 号：O175.7[理学—数学]