巴拿赫空间的吸引盆及其应用  

The Basin of Attraction in Banach Spaces and Its Applications

作　　者：王文相[1] 沈祖和[2] 

机构地区：[1]江苏省连云港财经高等职业技术学校,连云港222003 [2]南京大学数学系,南京210093

出　　处：《数学学报（中文版）》2006年第5期1013-1020,共8页Acta Mathematica Sinica：Chinese Series

摘　　要：利用吸引盆为工具,我们把巴拿赫空间的全局同胚问题转化为讨论纯量微分方程解的存在有限性．推广了Hadamard-Levy定理,并应用于区间分析和微分方程,推广了一些现有定理．By using the concept of Basin of Attraction as a main tool of our explosion in discussing the diffeomorphisms between Banach spaces, we change it into discussing the existence and finiteness of nonnegative solution of the scalar differential equation. In Section 2, an extension of the famous Hadamard-Levy theorem is given. In Section 3 and Section 4, the theorem is applied to interval analysis and differential equation respectively. The results of this paper generalize some existing theorems.

关 键 词：全局同胚 吸引盆 区间分析 

分 类 号：O241.81[理学—计算数学]