带有无穷求和的非线性离散不等式的推广及应用  

Nonlinear Discrete Inequalities with Infinite Summations and Their Applications

作　　者：邓圣福 李晓培 吴宇[2] DENG SHENGFU, LI XIAOPEI,WU Yu(1.School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, China;2.College of Mathematics, Yibin University, Yibin 644007, Chin)

机构地区：[1]岭南师范学院数学与统计学院,湛江524048 [2]宜宾学院数学学院,宜宾644007

出　　处：《应用数学学报》2018年第2期183-197,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金面上项目(11771197);广东省自然科学基金自由申请项目(2017A030313030);广东省高等学校高层次人才项目(QBS201501)资助

摘　　要：本文研究一类带有多个非线性项和无穷求和的二元离散不等式，借助数学归纳法，给出这类不等式中未知函数的估计，所得结果推广了一些已有结果．最后，本文利用此结果得到一个差分方程解的上界．Discrete inequalities involving two independent variables with more than one nonlinear term are discussed. The upper bound of the unknown function is given with the aid of the mathematical induction. The results obtained generalize some existed results. An application example to show the explicit bound of solutions of a difference equation is also given.

关 键 词：离散不等式 非线性 有界 

分 类 号：O178[理学—数学]