非连续弱紧增算子的不动点及其对Banach空间初值问题的应用

刘笑颖;吴从炘

系统科学与数学 ›› 2000, Vol. 20 ›› Issue (2) : 175-180.

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系统科学与数学 ›› 2000, Vol. 20 ›› Issue (2) : 175-180. DOI: 10.12341/jssms09776
论文

非连续弱紧增算子的不动点及其对Banach空间初值问题的应用

    刘笑颖,吴从炘
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FIXED POINT OF DISCONTINUOUS WEAKLY COMPACY INCREASING OPERATORS AND ITS APPLICATION TO INITIAL VALUE PROBLEM IN BANACH SPACES

    Xiao Ying LIU,Cong Xin WU
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摘要

证明了Banach空间上一类非连续的弱紧增算子的不动点定理,特别获得了最大不动点与最小不动点的存在性,改进了已有的某些结果.作为应用,讨论了Banach空间中含间断项的常微分方程初值问题最大解与最小解的存在性.

Abstract

The maximal and minimal fixed points theorems for a class of discontinuous weakly compact increasing operators in Banach spaces are proved,and some well-known results are improved.As an application,the existence of maximal and minimal solutions for the initial value problem of ordinary differential equations with discontinuous terms in Banach spaces is discussed.

关键词

相对弱紧 / 增算子 / 不动点 / 初值问题

Key words

Relatively weakly compact / increasing operators / maximal and minimal fixed points

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刘笑颖 , 吴从炘. 非连续弱紧增算子的不动点及其对Banach空间初值问题的应用. 系统科学与数学, 2000, 20(2): 175-180. https://doi.org/10.12341/jssms09776
Xiao Ying LIU , Cong Xin WU. FIXED POINT OF DISCONTINUOUS WEAKLY COMPACY INCREASING OPERATORS AND ITS APPLICATION TO INITIAL VALUE PROBLEM IN BANACH SPACES. Journal of Systems Science and Mathematical Sciences, 2000, 20(2): 175-180 https://doi.org/10.12341/jssms09776
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