一类推广的具有时滞的Pachpatte离散不等式及其应用

A GENERALIZED PACHPATTE'S DISCRETE INEQUALITY WITH DELAYS AND ITS APPLICATIONS

不仅把Pachpatte的离散不等式推广成时滞不等式,而且把不等式中的常数项推广成连续的正函数。推广后的不等式不仅包含了更多项,且不要求函数的单调性。利用单调化技巧给出了不等式中未知函数的估计。最后用得到的结果研究时滞差分方程初值问题解的唯一性与有界性。

In this paper, Pachpatte＇s discrete inequality is generalized to a retarded form, where not only delays are included but the contant term is generalized to a positive function. In the generalized inequality, there are more complex terms and the monotonicity of given functions is not required. Estimation of unknown function in the inequality is given by a technique of monotonization. Finally, the result is applied to discuss boundedness and uniqueness of solution for the initial value problem of a delay difference equation.