一类非线性差分不等式中未知函数的估计及其应用

数学物理学报 ›› 2015, Vol. 35 ›› Issue (5): 895-909.

一类非线性差分不等式中未知函数的估计及其应用

黄春妙, 王五生

河池学院数学与统计学院广西宜州 546300

收稿日期:2014-11-24 修回日期:2015-02-24 出版日期:2015-10-25 发布日期:2015-10-25
作者简介:王五生,wang4896@126.com
基金资助:
国家自然科学基金(11161018)和广西高校科学研究项目(KY2015ZD103,KY2015LX341)资助

Estimation of Unknown Function on A Class of Nonlinear Difference Inequality and Application

Huang Chunmiao, Wang Wusheng

School of Mathematics and Statistics, Hechi University, Guangxi Yizhou 546300

Received:2014-11-24 Revised:2015-02-24 Online:2015-10-25 Published:2015-10-25

摘要/Abstract

摘要：

该文建立了一类非线性差分不等式.此不等式包含了非线性函数与未知函数的复合函数,是一个具有多重和的差分不等式.利用单调技巧、放大方法、积分中值定理、变量替换技巧、差分和求和技巧,给出了未知函数的上界估计.最后,用所得结果研究了差分方程解的估计.

关键词: Volterra-Fredholm差分不等式, 多重和, 单调技巧, 积分中值定理, 估计

Abstract:

In this paper, we establish a class of nonlinear difference inequalities, where the inequalities consist of multiple iterated sums, and composite function of nonlinear function and unknown function. Firstly, the upper bounds of the unknown functions are given by technique of monotonization, amplification method, the mean-value theorem for integrals, technique of change of variable, difference and summation. Finally, we apply our derived results to the study of the estimation of solutions of difference equations.

Key words: Volterra-Fredholm type difference inequality, Multiple iterated sums, Technique of monotonization, The mean-value theorem for integrals, Estimation

中图分类号:

O178

黄春妙, 王五生. 一类非线性差分不等式中未知函数的估计及其应用[J]. 数学物理学报, 2015, 35(5): 895-909.

Huang Chunmiao, Wang Wusheng. Estimation of Unknown Function on A Class of Nonlinear Difference Inequality and Application[J]. Acta mathematica scientia,Series A, 2015, 35(5): 895-909.

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