x'=g(x,t)+h(t)型方程的拓扑动力系统与Kurzweil-Henstock积分  

Topological Dynamics of Equation of the form x' = g(x, t) + h(t) and Kurzweil-Henstock Integral

作　　者：李宝麟[1] 薛小平[2] 

机构地区：[1]西北师范大学数学系,兰州730070 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《数学学报（中文版）》2003年第4期795-804,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(19671021);NWNU-KJCXGC-212资助项目

摘　　要：本文借助Sell等人建立的局部动力系统理论,利用Kurzweil-Henstock积分,建立了x′=g(x,t)+h(t)型非自治微分方程的拓扑动力系统,为进一步讨论这种方程解的渐近行为作了基础性的工作.本文的工作也是Sell等人工作中有关结论的推广.By the theory of local dynamics system defined by Sell, by using the Kurzweil-Henstock integral, the local dynamics system of nonautonomous differential equations form x' = g(x, t) + h(t) is established. These results are of foundational significance of the works for further studying the asymptotic behavior of solutions of equations of the form x' = g(x,t) + hit). These results are also generalizations of some results in the works of Sell (see [1-12]).

关 键 词：Kurzweil-Henstock积分 局部动力系统 非自治微分方程 

分 类 号：O175.12[理学—数学]