一类含有未知函数差分的三重和差分不等式中未知函数的估计  

Estimation on the Unknown Function of a Class of Triple Sum-Difference Inequalities with Difference of the Unknown Function

作　　者：黄星寿 王五生 罗日才 HUANG Xingshou;WANG Wusheng;LUO Ricai(School of Mathematics and Statistics,Hechi University,Yizhou 546300,Guangxi)

机构地区：[1]河池学院数学与统计学院,广西宜州546300

出　　处：《四川师范大学学报（自然科学版）》2020年第2期219-224,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11961021);广西自然科学基金(2016GXNSFAA380090、2016GXNSFAA380125)。

摘　　要：Gronwall-Bellman型积分不等式的离散形式及其推广形式是研究和差分方程解的存在性、有界性和唯一性等定性性质的重要工具.研究一类非线性三重和差分不等式,和号内含有未知函数及其差分,和项外包含非常数项.利用差分和求和技巧、变量替换技巧和放大技巧等分析技巧,给出三重和差分不等式中未知函数的显上界估计,从而推广已有结果.最后通过一类和差分方程解估计的应用研究,印证所得结果的有用性.The discrete form and its generalizations of the Gronwall-Bellman type integral inequality are the important tools in the study of existence,boundedness and uniqueness and other qualitative properties of solutions of the sum-difference equations.This paper studies a class of nonlinear triple sum-difference inequalities,including an unknown function and its difference in sum term and a nonconstant factor outside sum term.The upper bounds of the unknown function in the triple sum-difference inequality is estimated explicitly by using difference and summing skills,change of variables,amplification,and other analysis techniques,which generalize some known results.Finally,in order to illustrate the usefulness of the results,the estimation of the solution of a class of difference equations is studied.

关 键 词：非线性三重和差分不等式 含有未知函数差分的求和项 和差分方程 显式估计 

分 类 号：O175.7[理学—数学]