一类二阶非线性差分方程的振动性  

Oscillation criteria for a family of second order nonlinear difference equations

作　　者：赵玉萍[1] 

机构地区：[1]青海民族大学数学学院,青海西宁810007

出　　处：《辽宁师范大学学报（自然科学版）》2012年第3期310-314,共5页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(10961020);国家民委科技计划项目(10QH03)

摘　　要：差分方程反映的是关于离散变量的变化规律.通过分析方程解的特别性质,可以把握离散变量的变化过程的规律.方程的振动性是研究方程定性理论的重要组成部分,从理论上探讨解的形态变化一直是近年来研究的热点.文章对已有文献中的线性差分方程进行了改进,研究了更普遍的方程,一类二阶非线性多时滞差分方程打振动性,利用分析的方法及积分中值定理,得到了该类方程振动的几个充分条件,并且应用差分方程的振动理论,研究了这类方程在特殊情形下解的一价差分的振动性,得到了一阶差分振动的充分条件,从而丰富了这类方程的研究成果.Difference equation reflects on the changing law of discrete variables. By analyzing the spe- cial nature of the equation, we can grasp the change regularity of discrete variables. Oscillation of e- quations is important components of the qualitative theory of equations. Theoretically studying on morphological changes of the solution is a hot research topic in recent years. In this paper, we has improved the linear difference equqture of literature, obtained more universal of equation. We con- cerned the oscillation criteria for a family of second order nonlinear multi delay difference equations, by usig the method of analysis and mean value theorem for the integral. We study several sufficient conditions for the oscillations of equations, the first equations, and establish sufficient conditions for the research results of this class equation. order difference of solution oscillation of special first order difference of oscillation, to enrich the

关 键 词：振动性 非线性 时滞 差分方程 

分 类 号：O175.7[理学—数学]