具正负系数和多变时滞的高阶非线性中立型差分方程非振动解的存在性  

Existence of nonoscillatory solutions of higher order nonlinear neutral difference equations with positive and negative coefficients and multiple variable delays

作　　者：张萍 覃桂茳 杨甲山 ZHANG Ping;QIN Guijiang;YANG Jiashan(School of Science,Shaoyang University,Shaoyang 422004,Hunan Province,China;School of Data Science and Software Engineering,Wuzhou University,Wuzhou 543002,Guangxi Zhuang Autonomous Region,China)

机构地区：[1]邵阳学院理学院,湖南邵阳422004 [2]梧州学院大数据与软件工程学院,广西梧州543002

出　　处：《浙江大学学报（理学版）》2022年第1期41-48,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(51765060);湖南省教育厅一般项目(20C1683);广西高校中青年教师基础能力提升项目(2018KY0543,2020KY17007)。

摘　　要：利用Banach空间的不动点原理和不等式技巧,研究具正负系数和多变时滞的高阶非线性中立型差分方程正解的存在性,在一定条件下,建立了该方程的新的非振动准则,所得结论推广并改进了一系列已有结果。By using the fixed point theorem in Banach space and the inequality technique,we discuss the existence of positive solution for a class of higher order nonlinear neutral difference equations with positive and negative coefficients and multiple variable delays.Under certain conditions,we establish a few new nonoscillation criteria.Our results improve and extend some known results.

关 键 词：正负系数 多变时滞 高阶非线性中立型差分方程 非振动 不动点定理 

分 类 号：O175.7[理学—数学]