一类乘积形式的离散不等式及其应用

A Class of Discrete Inequality of Product Form

该文在文献[2]的基础上,研究了一类新的乘积形式的离散不等式.把参考文献中不等式右端第一个因子中包含的未知函数u推广成未知函数的幂函数u^2,运用变量替换技巧、放大技巧、微分中值定理、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.最后,阐述了所得的结果可以用来给出乘积形式差分方程解的绝对值的上界估计.

In this paper, we study a class of new discrete inequality of product form on the basis of the literature [2]. Our discrete inequality contains compound function of power function and unknown function in sum, but the discrete inequalities in reference only contains the linear factor of unknown function. The estimation of unknown function in our inequality are given by technique of change of variable, amplification method, difference and summation, inverse function, and the dialectical relationship between constants and variables. Finally, we expound that we can give estimation of solutions of a class of difference equation of product form by our result.