非线性三变量差分不等式及其应用  

Nonlinear Difference Inequalities in Three Variables and Their Applications

作　　者：侯宗毅[1] 王五生[1] 

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）》2015年第4期514-517,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11161018);广西省自然科学基金(2012GXNSFAA053009);广西高等学校科研项目(KY2015ZD103)

摘　　要：在文献(B.G.Pachpatte.Demonstratio Math,2009,XLII:341-351.)的基础上,建立了一类新的三变量非线性差分不等式.把参考文献中不等式右端和中的乘积因子u推广成u的非线性函数.运用变量替换技巧、放大技巧、积分微分技巧、反函数技巧、常量与变量的辩证关系,给出了不等式中未知函数的估计,推广了文献中相应不等式的结果.最后,用所得结果给出了三变量差分方程解的估计.In this paper, we study a new nonlinear difference inequality in three variables on the basis of the literature （B. G. Pachpatte. Demonstratio Math ,2009, XLII：341-351. ）. Our difference inequality contains nonlinear factor of unknown function in summation, but the difference inequality in reference only contains the linear factor of unknown function. The estimation of unknown function in our difference inequality is given by using technique of change of variable, amplification method, integration and differentiation, inverse function, and the dialectical relationship between constants and variables. Furthermore, the corresponding result in the literature is particular case of our result. Finally, we apply our result to give estimation of solutions of a difference equation in three variables.

关 键 词：三变量差分不等式 不等式技巧 差分方程 解的估计 

分 类 号：O175.5[理学—数学]