Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
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DOI：
10.1137/1018114
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发表时间：
1976-10
期刊：
影响因子：
10.2
通讯作者：
H. Amann
中科院分区：
文献类型：
--
作者：
H. Amann
本文综述了序Banach空间中非线性泛函分析的一些最重要的方法和结果。利用迭代技巧和拓扑工具，得到了序Banach空间中全连续映射的不动点定理，并特别注意了多重性结果的推导.进一步研究了非线性依赖于一个真实的参数的不动点方程的可解性和分支问题，为了说明抽象结果的重要性，给出了非线性椭圆边值问题的一些非平凡应用.但是，当然，本文的抽象技术和结果也适用于各种其他问题，这是不考虑在这里。本文提出了一个统一的方式在这一领域的最新工作。此外，利用紧映射的不动点指数，得到了大多数“经典”定理的简短证明。
This paper gives a survey over some of the most important methods and results of nonlinear functional analysis in ordered Banach spaces. By means of iterative techniques and by using topological tools, fixed point theorems for completely continuous maps in ordered Banach spaces are deduced, and particular attention is paid to the derivation of multiplicity results. Moreover, solvability and bifurcation problems for fixed point equations depending nonlinearly on a real parameter are investigated.In order to demonstrate the importance of the abstract results, there are given some nontrivial applications to nonlinear elliptic boundary value problems. But, of course, the abstract techniques and results of this paper apply also to a variety of other problems which are not considered here.This paper presents in a unified manner most of the recent work in this field. In addition, by making consequent use of the fixed point index for compact maps, short and simple proofs are obtained for most of the “classical” r...