K－集压缩向量场产生的局部流是压缩的局部集

LOCAL FLOW GENERATED BY A K-SET-CONTRACTION VECTOR ISA LOCAL SET-CONTRACTION

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.