用于边界值问题的拓扑不动点原理

所属分类:数学  
出版时间:2011-7   出版时间:世界图书出版公司   作者:安德里斯   页数:761  

内容概要

  安德里斯编著的《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。本书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。

书籍目录

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

章节摘录

版权页:
插图:
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.

编辑推荐

《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。

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  •     很好的书,有用,仔细学习
 

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