摘要
设X是Banach空间,f:X→X是局部Lipschitz映射,σ是由方程σ(x,t)=-f(σ(x,t)),σ(x,0)=x产生的局部流。本文证明了当f=I-F为K-集-压缩向量场时,在局部、对于充分小的正数t0,映射σ(·,t0)是集一压缩映射.且σ的孤立不动点的指教等于F在此点的不动点指教。
Let X be a Banach space. then f:X→X is a local lipschitzion and σ-the local flow generated by eqtiations σ(x,t)=-f(σ(x,t))and σ(x,0)=x In this paper,it has been proved thatif f=I-F is a k-set-contraction vector field,then,locally, for every,sufficiently small posi- tive number to,the mapping σ(·,t0)is a set-contraction and the index of σ at an isolated fixed point is equal to the index of F at this point.
出处
《内蒙古工业大学学报(自然科学版)》
1995年第2期5-8,共4页
Journal of Inner Mongolia University of Technology:Natural Science Edition
关键词
拓扑度
局部集
向量场
巴拿赫空间
Lipschitzion
topologic degree
conley’s index theory