一类具正负系数的高阶泛函差分方程的振荡性  

Oscillation of Certain Higher-Order Functional Difference Equations with Positive and Negative Coefficients

作　　者：杨甲山[1,2] 覃桂茳[1,2] YANG Jia-shan1,2, QIN Gui-jiang1,2(1. School of Information and Electronic Engineering, Wuzhou University, Wuzhou 543002, China ;2. Laboratory of Complex System Simulation and Intelligent Computing, Wuzhou University, Wuzhou 543002, Chin)

机构地区：[1]梧州学院信息与电子工程学院,广西梧州543002 [2]梧州学院复杂系统仿真与智能计算实验室,广西梧州543002

出　　处：《数学的实践与认识》2018年第6期290-297,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(51765060);硕士学位授予单位立项建设项目(桂学位[2013]4号)

摘　　要：研究了一类具有正负系数和多变时滞的高阶非线性中立型泛函差分方程的振荡性，利用Banach空间的不动点原理和广义的Riccati变换，获得了该类方程存在非振荡解的新准则，并同时得到了该类方程振荡的新的充分条件，这些准则改善了对方程的条件限制，所得定理推广并改进了现有文献中的一系列结果．The oscillation for a class of higher-order nonlinear neutral functional difference equations with with positive and negative coefficients and multi-time delay was discussed in this article. By using the fixed point theorem in Banach space and the generalized Riccati transformation, a new nonoscillation criteria for the equations was obtained. In addition, a new nosciUation criteria for the equations was proposed. These criteria could improve the restriction of the conditions for the equations. Some existed results in the literatures have been further improved and extended.

关 键 词：振荡和非振荡 正负系数 中立型泛函差分方程 多变时滞 不动点原理 RICCATI变换 

分 类 号：O175.7[理学—数学]