内容简介
用于边界值问题的拓扑不动点原理（英文版）
作者：（捷克）安德里斯 著
出版时间：2011年版
内容简介
《用于边界值问题的拓扑不动点原理》旨在系统介绍凸空间上的单值和多值映射的拓扑不动点理论。内容包括常微分方程的边界值问题和在动力系统中的应用，是第一本用非度量空间讲述拓扑不动点理论的专著。尽管理论上的讲述和书中精选的应用实例相结合，但本身具有很强的独立性。《用于边界值问题的拓扑不动点原理》利用不动点理论求微分方程的解，独具特色。目次：理论背景；一般原理；在微分方程中的应用。
目录
preface
scheme for the relationship of singlc sections
chapter Ⅰ
Theoretical background
Ⅰ.1.structure of locally convex spaces
Ⅰ.2.anr-spaces and ar-spaces
Ⅰ.3.multivadued mappings and their selections
Ⅰ.4.admissible mappings
Ⅰ.5.special classes of admissible mappings
Ⅰ.6.lefschetz fixed point theorem for admissible mappings
Ⅰ.7.lefschetz fixed point theorem for condensing mappings
Ⅰ.8.fixed point index and topological degree for admissible maps in locally convex spaces
Ⅰ.9.noncon pact case
Ⅰ.10.nielsen number
Ⅰ.11.nielsen number; noncompact case
Ⅰ.12.remarks and comments
chapter Ⅱ
General principles
II.1.topological structure of fixed point sets: aronszajn-browder-gupta-type results
Ⅱ.2.topological structure of fixed point sets: inverse limit method
Ⅱ.3.topological dimension of fixed point sets
Ⅱ.4.topological essentiality
Ⅱ.5.relative theories of lefschetz and nielsen
Ⅱ.6.periodic point principles
Ⅱ.7.fixed point index for condensing maps
Ⅱ.8.approximation methods in the fixed point theory of multivalued mappings
Ⅱ.9.topological degree defined by means of approximation methods
Ⅱ.10.continuation principles based on a fixed point index
Ⅱ.11.continuation principles based on a coincidence index
Ⅱ.12.remarks and comments
chapter Ⅲ
Application to differential equations and inclusions
Ⅲ.1.topological approach to differential equations and inclusions
Ⅲ.2.topological structure of solution sets: initial value problems
Ⅲ.3.topological structure of solution sets: boundary value problems
Ⅲ.4.poincare operators
Ⅲ.5.existence results
Ⅲ.6.multiplicity results
Ⅲ.7.wakewski-type results
Ⅲ.8.bounding and guiding functions approach
Ⅲ.9.infinitely many subharmonics
Ⅲ.10.almost-periodic problems
Ⅲ.11.some further applications
Ⅲ.12.remarks and comments
Appendices
A.1.almost-periodic single-valued and multivalued functions
A.2.derivo-periodic single-valued and multivalued functions
A.3.fractals and multivalued fractals
references
index