两类稳定性定理的改进  

Improvements of Two Kinds of Stability Theorems

作　　者：杨墨[1] 范英飞 

机构地区：[1]西南交通大学数学学院,成都610031

出　　处：《数学理论与应用》2017年第1期50-56,共7页Mathematical Theory and Applications

摘　　要：本文对两类稳定性定理进行了改进.通过K函数性质,将原来马尔金稳定性定理中V函数导数在有限时间内可变号的性质,推广到长时间内,得到了新的非自治微分方程解的稳定性判定方法.对积分收敛判定定理中的不足进行了补充说明,并且对定理进行了改进和推广,得到了新的一致稳定性判定方法.In this paper, two kinds of stability theorems are improved. By the property of the K function, the property of the function＇s derivative in original Markin stability theorem is extended from the finite time to the infinite time, and this brings the new method to get the stability of the solution of the nonautonomous differen- tial equation. By the supplement of the integral convergence theorem , the new theorem is further improved and promoted, and a new determination method about uniform stability is obtained.

关 键 词：马尔金 稳定性 积分收敛 一致稳定性 

分 类 号：O175[理学—数学]