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Global solution curves for semilinear elliptic equations
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Description
Rating
Title
Global
solution
curves
for
semilinear
elliptic
equations
Creator
Korman, Philip.
Contributors
World Scientific (Firm)
DescriptionAbstract
This
book
provides
an
introduction
to the
bifurcation
theory
approach
to
global
solution
curves
and
studies
the
exact
multiplicity
of
solutions
for
semilinear
Dirichlet
problems
,
aiming
to
obtain
a
complete
understanding
of the
solution
set
. This
understanding
opens
the
way
to
efficient
computation
of
all
solutions
.
Detailed
results
are
obtained
in
case
of
circular
domains
, and
some
results
for
general
domains
are also
presented
. The
author
is
one
of the
original
contributors
to the
field
of
exact
multiplicity
results
.
DescriptionTable Of Contents
1
.
Curves
of
solutions
on
general
domains
.
1.1
.
Continuation
of
solutions
.
1.2
.
Symmetric
domains
in
R[symbol]
.
1.3
.
Turning
points
and the
Morse
index
.
1.4
.
Convex
domains
in
R[symbol]
.
1.5
.
Pohozaev's
identity
and
nonexistence
of
solutions
for
elliptic
systems
.
1.6
.
Problems
at
resonance

2
.
Curves
of
solutions
on
balls
.
2.1
.
Preliminary
results
.
2.2
.
Positivity
of
solution
to the
linearized
problem
.
2.3
.
Uniqueness
of the
solution
curve
.
2.4
.
Direction
of a
turn
and
exact
multiplicity
.
2.5
. On a
class
of
concaveconvex
equations
.
2.6
.
Monotone
separation
of
graphs
.
2.7
. The
case
of
polynomial
f(u)
in
two
dimensions
.
2.8
. The
case
when
f(0)
<
0.
2.9
.
Symmetry
breaking
.
2.10
.
Special
equations
.
2.11
.
Oscillations
of the
solution
curve
.
2.12
.
Uniqueness
for
nonautonomous
problems
.
2.13
.
Exact
multiplicity
for
nonautonomous
problems
.
2.14
.
Numerical
computation
of
solutions
.
2.15
.
Radial
solutions
of
Neumann
problem
.
2.16
.
Global
solution
curves
for a
class
of
elliptic
systems
.
2.17
. The
case
of a "
thin
"
annulus
.
2.18
. A
class
of
pLaplace
problems

3
.
Two
point
boundary
value
problems
.
3.1
.
Positive
solutions
of
autonomous
problems
.
3.2
.
Direction
of the
turn
.
3.3
.
Stability
and
instability
of
solutions
.
3.4
.
Sshaped
solution
curves
.
3.5
.
Computing
the
location
and the
direction
of
bifurcation
.
3.6
. A
class
of
symmetric
nonlinearities
.
3.7
.
General
nonlinearities
.
3.8
.
Infinitely
many
curves
with
pitchfork
bifurcation
.
3.9
. An
oscillatory
bifurcation
from
zero
: a
model
example
.
3.10
.
Exact
multiplicity
for
Hamiltonian
systems
.
3.11
.
Clamped
elastic
beam
equation
.
3.12
.
Steady
states
of
convective
equations
.
3.13
.
Quasilinear
boundary
value
problems
.
3.14
. The
time
map
for
quasilinear
equations
.
3.15
.
Uniqueness
for a
pLaplace
case
.
Publisher
World Scientific Pub. Co.
Subject
Bifurcation theory.
Mathematical analysis.
Elliptic functions.
Dirichlet problem.
Identifier
9789814374354
(electronic
bk.)
;
9814374342
;
9789814374347
;
http://www.worldscientific.com/worldscibooks/10.1142/8308#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xi, 241 p. : ill. (some col.)
Date
c2012
.
OCLC number
874498100
CONTENTdm number
393
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