一类和号内含有未知函数差分的和差分不等式中未知函数的估计  

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

作　　者：范乐乐 FAN Lele(School of Mathematics and Statistics,Hechi University,Yizhou,Guangxi 546300,China)

机构地区：[1]河池学院数学与统计学院

出　　处：《南华大学学报（自然科学版）》2019年第5期60-63,共4页Journal of University of South China：Science and Technology

基　　金：广西省自然科学基金项目(2016GXNSFAA380090);河池学院2019年校级青年课题(2019XJQN009)

摘　　要：研究了一类Gronwall-Bellman型非线性和差分不等式,和号内不仅含有未知函数而且含有未知函数的差分,和项外具有非常数项因子。利用变量替换技巧和放大技巧等分析手段,给出了和差分不等式中未知函数的显式估计,最后结合实例说明所得的结果可以用来研究一类和差分方程解的定性性质。This paper studies a class of nonlinear sum-difference inequalities,which include an unknown function and its difference in summation term and a nonconstant factor outside summation term.The upper bound of the unknown function in the sum-difference inequality is estimated explicitly using various analytical means including the change and amplification of variables.Finally,an example is given to illustrate that the results can be used to study the qualitative properties of solutions of sum-difference equations.

关 键 词：非线性和差分不等式 变量替换和放大技巧 显式估计 和差分方程 

分 类 号：O175.5[理学—数学]