具正负系数的二阶非线性中立型时滞差分方程的非振动准则  

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

作　　者：杨甲山[1] 方彬[2] 

机构地区：[1]邵阳学院理学与信息科学系,湖南邵阳422004 [2]信阳师范学院数学与信息科学学院,河南信阳464000

出　　处：《邵阳学院学报（自然科学版）》2011年第1期1-4,共4页Journal of Shaoyang University：Natural Science Edition

基　　金：湖南省教育厅科研重点项目(09A082)

摘　　要：近年来,随着科学技术的发展,差分方程理论不仅在物理学、航天卫星等领域中有重要的应用,而且在经济学、生物学、控制理论等自然科学和社会科学领域也成为不可缺少的数学工具.而中立型差分方程的振动性与非振动性理论作为中立型差分方程定性理论中的重要内容,更是受到了人们的普遍关注.本文研究了一类具有正负系数的二阶非线性中立型差分方程正解的存在性,利用Banach空间的不动点原理,结合一些分析技巧,得到了这类方程存在有界的最终正解的充分条件,推广并改进了现有文献中的结论.同时给出例子验证其有效性.In recent years,with the development of science and technology,the difference equation theory not only has important applications in such fields as physics,space satellite,etc.,but also has become an indispensable mathematics tool in such natural science and domain of the social sciences as economics,biology,control theory,etc..Moreover,oscillation and nonoscillation theory being the key content of qualitative study of the neutral difference equations,it gets prevalent attention of people.In this paper,the existence of positive solution for a class of second order nonlinear neutral delay difference equations with positive and negative coefficients is studied.Using the fixed point theorem in Banach space and some necessary analytic techniques,the sufficient conditions for the existence of eventually positive solutions are obtained.Some existing results in the literature are improved and extended.The examples are presented to illustrate the effects of our theorems.

关 键 词：正负系数 非线性 中立型时滞差分方程 不动点原理 最终正解 

分 类 号：O175.7[理学—数学]