用于邊界值問題的拓?fù)洳粍狱c(diǎn)原理

內(nèi)容概要

　　安德里斯編著的《用于邊界值問題的拓?fù)洳粍狱c(diǎn)原理》旨在系統(tǒng)介紹凸空間上的單值和多值映射的拓?fù)洳粍狱c(diǎn)理論。內(nèi)容包括常微分方程的邊界值問題和在動力系統(tǒng)中的應(yīng)用，是第一本用非度量空間講述拓?fù)洳粍狱c(diǎn)理論的專著。盡管理論上的講述和書中精選的應(yīng)用實(shí)例相結(jié)合，但本身具有很強(qiáng)的獨(dú)立性。本書利用不動點(diǎn)理論求微分方程的解，獨(dú)具特色。目次：理論背景；一般原理；在微分方程中的應(yīng)用。

書籍目錄

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

章節(jié)摘錄

版權(quán)頁：   插圖：   Our book is devoted to the topological fixed point theory both for single—valued and multivalued mappings in locally convex spaces， including its application to boundary value problems for ordinary differential equations （inclusions） and to （multivalued） dynamical systems． It is the first monograph dealing with the topological fixed point theory in non—metric spaces． Although the theoretical material was tendentially selected with respect to applications， we wished to have a self—consistent text （see the scheme below）． Therefore， we supplied three appendices concerning almost—periodic and derivo—periodic single—valued （multivalued） functions and （multivalued） fractals． The last topic which is quite new can be also regarded as a contribution to the fixed point theory in hyperspaces． Nevertheless， the reader is assumed to be at least partly familiar in some related sections with the notions like the Bochner integral， the Aumann multivalued integral， the Arzela—Ascoli lemma， the Gronwall inequality， the Brouwer degree， the Leray—Schauder degree， the topological （covering） dimension， the elemens of homological algebra，．．．Otherwise， one can use the recommended literature． Hence， in Chapter I， the topological and analytical background is built． Then， in Chapter II （and partly already in Chapter I）， topological principles necessary for applications are developed， namely： —the fixed point index theory （resp． the topological degree theory）， —the Lefschetz and the Nielsen theories both in absolute and relative cases， —periodic point theorems， —topological essentiality， —continuation—type theorems． All the above topics are related to various classes of mappings including compact absorbing contractions and condensing maps． Besides the （more powerful） homological approach， the approximation techniques are alternatively employed as well．

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《用于邊界值問題的拓?fù)洳粍狱c(diǎn)原理》利用不動點(diǎn)理論求微分方程的解，獨(dú)具特色。目次：理論背景；一般原理；在微分方程中的應(yīng)用。

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