Banach空间中Cauchy初值问题解的存在性

The Existence of Solutions for Cauchy' s Initial Value Problem in Banach Spaces

中文关键词:  Cauchy初值问题  紧型条件  闭集上的解

英文关键词:Cauchy problem  compactness type conditions  solution in closed set

中文摘要:

      在研灾Banach空间常微分方程Cauchy 问题解的存在性问题时,人们常常使用一个 很难验证且一般情况下难以达到的条件──一致连续性条件,本文完全不使用一致连续性条 件,仅利用紧型条件,获得了Banach空间Cauchy问题解的存在性定理,从而改进和推广了已 知的有关结果,

英文摘要:

      In this paper, the author obtains some existence theorems for Cauchy's initial val-ue problems in Banach spaces, The main characteristic of this paper is that the author do not employ uniform continuity condition, The results in this paper are improvements and gener-alizations of the known ones,