一类新的非线性和差分不等式及其应用  

A NEW NONLINEAR SUM-DIFFERENCE INEQUALITY AND ITS APPLICATION

作　　者：王五生[1] 李自尊[2] 

机构地区：[1]河池学院数学系,宜州546300 [2]百色学院数学与计算机信息工程系,百色533000

出　　处：《系统科学与数学》2012年第2期181-189,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11161018);广西自然科学基金(0991265);广西教育厅科学研究基金(201106LX599);河池学院基金(2009YAZ-N001;200725)资助课题

摘　　要：由于差分不等式是研究差分方程解的存在性、有界性、唯一性、稳定性等定性性质的重要工具,许多数学家不仅研究Gronwall类积分不等式的各种推广形式及其应用,而且研究差分不等式及其应用.该文建立了一类新的非线性和差分不等式,利用分析技巧给出了不等式中未知函数的上界估计.将得到的结果应用到时滞差分方程的边值问题,得到了差分方程解的估计.Difference inequalities are important tools in the study of existence,uniqueness, boundedness,stability and other qualitative properties of solutions of difference equations. Many mathematicians not only study various generalizations of Gronwall inequality and their applications,but also study various difference inequalities.In this paper,we establish a new nonlinear sum-difference inequality,and the estimation of unknown function in the inequality is given by using a analytic technique.Furthermore,the result is used to boundary value problems of retarded difference equations and to get the estimation of solutions of the difference equation.

关 键 词：和差分不等式 差分方程 解的估计 

分 类 号：O178[理学—数学]