高维系统周期解的存在性与唯一性

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF HIGHER DIMENSIONAL SYSTEMS

本文首先利用一种新方法讨论高维系统解的一致有界性，一致最终有界性及非常稳定性问题，然后将所获结果应用于高维系统周期解的存在性与唯一性的研究．另外，木文还提出了“阶梯形系统”的概念，并对其建立了一种利用系统部分方程周期解存在性判定整个系统周期解存在性的方法．

in this paper, we first use a new method to obtain some new results concerningthe uniform boundedness, uniformly ultimate boundedness and extreme stability of solutionsof higher dimensional systems. And then using these results we study the etistence anduniqueness of periodic solutions of higher dimensional systems. On the other hand, we alsointroduce the concept of 'ladderlike system' and present an approach to study the existenceof periodic solutions for such system.