具正负系数的二阶中立型时滞差分方程的振动和非振动准则  

Oscillation and Nonoscillation Criteria for Second Order Neutral Delay Difference Equations with Positive and Negative Coefficients

作　　者：杨甲山[1] 李继猛[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：《数学的实践与认识》2012年第3期241-248,共8页Mathematics in Practice and Theory

基　　金：湖南省教育厅资助科研项目(07C680)

摘　　要：研究了一类具有正负系数的二阶非线性中立型时滞差分方程的振动性,利用Banach空间的不动点原理,结合Riccati变换,获得了该类方程存在非振动解的一些新的准则,并同时得到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.Oscillation for a class of the second order nonlinear neutral delay difference equation with positive and negative coefficients was considered . Using the fixed point theorem in Banach space and the generalized Riccati transformation , some new nonoscillation criteria for the equation were obtained , moreover some sufficient conditions for oscillatory of the equation were given , these criteria can improve the restriction of the conditions for the equation . Some existing results in the literature have been improved and extended.

关 键 词：正负系数 中立型时滞差分方程 非线性 振动和非振动 RICCATI变换 

分 类 号：O175.7[理学—数学]