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Generalized ordinary differential equations : not absolutely continuous solutions
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Description
Rating
Title
Generalized
ordinary
differential
equations
: not
absolutely
continuous
solutions
Creator
Kurzweil, Jaroslav.
Contributors
World Scientific (Firm)
DescriptionAbstract
This
book
provides
a
systematic
treatment
of the
Volterra
integral
equation
by
means
of a
modern
integration
theory
which
extends
considerably
the
field
of
differential
equations
.
It
contains
many
new
concepts
and
results
in the
framework
of a
unifying
theory
. In
particular
, this
new
approach
is
suitable
in
situations
where
fast
oscillations
occur
.
DescriptionTable Of Contents
1
.
Introduction

2
.
Kapitza's
pendulum
and a
related
problem

3
.
Elementary
methods
:
averaging

4
.
Elementary
methods
:
internal
resonance

5
.
Strong
Riemannintegration
of
functions
of a
pair
of
coupled
variables

6
.
Generalized
ordinary
differential
equations
:
strong
Riemannsolutions
(concepts)

7
.
Functions
[symbol]
,
[symbol]

8
.
Strong
Riemannsolutions
of
generalized
differential
equations
: a
survey

9
.
Approximate
solutions
:
boundedness

10
.
Approximate
solutions
: a
Lipschitz
condition

11
.
Approximate
solutions
:
convergence

12
.
Solutions

13
.
Continuous
dependence

14
.
Strong
Kurzweil
Henstockintegration
of
functions
of a
pair
of
coupled
variables

15
.
Generalized
differential
equations
:
Strong
Kurzweil
Henstocksolutions

16
.
Uniqueness

17
.
Differential
equations
in
classical
form

18
. On a
class
of
differential
equations
in
classical
form

19
.
Integration
and
Strong
integration

20
. A
class
of
Strong
Kurzweil
Henstockintegrable
functions

21
.
Integration
by
parts

22
. A
variant
of
Gronwall
inequality

23
.
Existence
of
solutions
of a
class
of
generalized
ordinary
differential
equations

24
. A
convergence
process
as a
source
of
discontinuities
in the
theory
of
differential
equations

25
. A
class
of
Strong
Riemannintegrable
functions

26
. On
equality
of
two
integrals

27
. A
class
of
generalized
ordinary
differential
equations
with a
restricted
right
hand
side
.
Publisher
World Scientific Pub. Co.
Subject
Differential equations.
Mathematical analysis.
Identifier
9789814324038
(electronic
bk.)
;
9814324027
;
9789814324021
;
http://www.worldscientific.com/worldscibooks/10.1142/7907#t=toc
Language
eng
Type
Electronic books.
FormatExtent
ix, 197 p. : ill.
Date
c2012
.
RelationIs Part Of
Series in real analysis
11
OCLC number
874501247
CONTENTdm number
306
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