变系数高阶中立型差分方程非振动解的存在性  

Existence of nonoscillatory solutions of higher-order neutral difference equations with variable coefficients

作　　者：沈洁[1] 郭瑞霞[1] 曾雪[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2011年第2期142-145,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学技术研究项目(L2010235)

摘　　要：差分方程在实际中具有广泛的应用背景,近年来许多学者对其展开了研究,取得了一些成果.主要研究了形如Δm(xn+cxn-k)+pnxn-r-qnxn-l=0,n≥n0∈{0,1,2,…}的变系数高阶中立型时滞差分方程非振动解的存在性问题,其中c∈R,m≥1,k≥1,l≥0是整数,{pn}n∞=n0,{qn}∞n=n0是2个非负的实数数列.根据上述方程,我们首先定义了巴拿赫空间中的一个有界闭凸子集以及在其上的一个映射,然后通过证明该映射是自映射和压缩映射,从而由巴拿赫压缩映射原理得到了上述方程存在非振动解的充分条件,其中c可以取除去1之外的任何值,本文结果推广了文献[1]中已有的某些结论.Since difference equation has wide applications in many fields,lots of authors pay more attention to the study of this kind of problems,and many good results have been obtained.This paper considers the following variable coefficients higher-order neutral delay difference equationsΔm（xn＋cxn-k）＋pnxn-r-qnxn-l=0,n≥n0∈{0,1,2,…}where c∈R,m≥1,k≥1,r,l≥0 are integers,{pn}∞n=n0,{qn}∞n=n0 are two sequences of nonnegative real numbers.Firstly,we define a closed bounded and convex subset of Banach space and a mapping on this subset and prove this mapping is a contraction operator.By using Banach contraction principle,we obtain some sufficient conditions for the results of nonoscillatory solutions of this equation with different value of c（c≠1）.The results obtained in this paper generalize some in conclusion[1].

关 键 词：中立型差分方程 非振动解 巴拿赫压缩映射原理 不动点 

分 类 号：O177.91[理学—数学]