On Krasnoselskii's Cone Fixed Point Theorem
On Krasnoselskii's Cone Fixed Point Theorem
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关于 Krasnoselskii 圆锥不动点定理
DOI：
10.1155/2008/164537
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发表时间：
2008
影响因子：
--
通讯作者：
M. Kwong
中科院分区：
文献类型：
--
作者：
M. Kwong
近年来，锥映射的Krasnoselskii不动点定理及其许多推广已被成功地应用于研究各种类型的边值问题的多重解的存在性。在本文的第一部分中，我们重温Krasnoselskii定理，在一个更拓扑的角度来看，并表明它可以推导出一个基本的方式从经典的Brouwer-Schauder定理。这一观点也导致了一个拓扑理论的推广定理。在本文的第二部分中，我们扩展了锥定理在不同的方向使用的概念收缩，并表明，一个更强的形式经常引用的Leggett-Williams定理是这种扩展的一个特例。
In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.