投影下的离散Gronwall不等式的推广及应用

A generalization of a projected discrete Gronwall's inequality and application

投影下的离散Gronwall不等式是研究具有指数二分性的差分方程的重要工具.为了研究非指数型增长的不变分解,本文将投影下的离散Gronwall不等式的一些结果推广到包括比指数型增长更弱的更一般的情形.进而,将它用于一个具有弱增长率的不变分解的差分方程,给出其有界解的估计.

The projected discrete Gronwall＇s inequality is an important tool for investigating difference equations with exponential dichotomy. In order to study invariant decomposition of non-exponential growth, in this paper, a projected discrete Gronwall＇s inequality is generalized to a more general one with weakly exponential growth. And then, these results is used to estimate hounded solutions of difference equations with invariant decomposition of weak growth rate.