一类和号内含有未知函数差分的二重和差分不等式中未知函数的估计  

Estimation of Unknown Function of a Class of Double Sum-Difference Inequalities with Difference of Unknown Function

作　　者：黄星寿 王五生 罗日才 HUANG Xing-shou;WANG Wu-sheng;LUO Ri-cai(School of Mathematics and Statistics,Hechi University,Yizhou 546300,China)

机构地区：[1]河池学院数学与统计学院,广西宜州546300

出　　处：《中北大学学报（自然科学版）》2018年第6期642-647,共6页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11561019;11161018);广西自然科学基金项目(2016GXNSFAA380090;2016GXNSFAA380125)

摘　　要：研究了一类非线性二重和差分不等式,和号内含有未知函数及其差分,和项外包含非常数项.利用变量替换技巧、放大技巧和积分中值定理等分析技巧,给出了二重和差分不等式中未知函数的显上界估计,从而推广了已有结果.为了说明所得结果的有用性,最后研究了一类和差分方程解的估计.得到的结果可以用来研究差分方程解的存在性、有界性和唯一性等定性性质.A class of nonlinear double sum-difference inequalities was investigated,which included an unknown function and its difference in summation term and a nonconstant factor outside summation term.The upper bounds of the unknown function in the double sum-difference inequality was estimated explicitly using the techniques of change of variable,the method of amplification,the integral mean value theorem,and other analysis techniques,which generalized some known results.Finally,in order to illustrate the usefulness of the results,the estimation of the solution of a class of sum difference equations was studied.The obtained results can be used to study the existence,boundedness and uniqueness of solutions of differential equations.

关 键 词：非线性二重和差分不等式 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]