基于不动点理论的微分系统解的有界性与实用稳定性  

Boundedness and Practical Stability for Differential Systems Based on Fixed Point Theory

作　　者：杨涛[1] 周英告[1,2] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410083 [2]中南大学信息科学与工程学院,湖南长沙410083

出　　处：《四川师范大学学报（自然科学版）》2011年第3期296-299,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10771215)资助项目

摘　　要：使用推广了的Gronwall-Bellman不等式,结合Leray-Schauder不动点定理研究了一类微分方程解的存在性与有界性问题,获得了一些新的充分性条件,所得结果推广并改进了已有文献中的一些结论;并运用Leray-Schauder不动点理论探讨了系统在给定区间上的实用稳定性问题,克服了传统方法中构造Lia-punov函数的困难,进而得到了一些系统实用稳定性的充分条件.The existence and boundedness of solutions for a kind of differential system are studied by using the extended Gronwall-Bellman＇s inequality and Leray-Schauder＇s fixed point theorem.Some new sufficient conditions are obtained.The known results in the literature are extended and improved.The pratical stability of the solutions for the differential system on the given interval are studied by Leray-Schauder＇s fixed theorem,which overcome the difficulties of constructing the Liapunov function in the traditional method,and some new conditions for the practical stability are obtained.

关 键 词：LERAY-SCHAUDER不动点定理 GRONWALL-BELLMAN不等式 有界性 实用稳定性 

分 类 号：O175.13[理学—数学]