Morse index of solutions of nonlinear elliptic equations
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| Format: | Buch |
| Sprache: | English |
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Berlin
De Gruyter
[2019]
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| Schriftenreihe: | De Gruyter series in nonlinear analysis and applications
Volume 30 |
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| LEADER | 00000nam a2200000 cb4500 | ||
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| 020 | |a 9783110537321 |c hardcover |9 978-3-11-053732-1 | ||
| 020 | |a 311053732X |9 3-11-053732-X | ||
| 035 | |a (OCoLC)1128840839 | ||
| 035 | |a (DE-599)DNB1175757349 | ||
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| 100 | 1 | |a Damascelli, Lucio |e Verfasser |0 (DE-588)1191192431 |4 aut | |
| 245 | 1 | 0 | |a Morse index of solutions of nonlinear elliptic equations |c Lucio Damascelli and Filomena Pacella |
| 264 | 1 | |a Berlin |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a XV, 254 Seiten |b Illustrationen, Diagramme |c 25 cm, 603 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v Volume 30 | |
| 650 | 0 | 7 | |a Nichtlineare elliptische Differentialgleichung |0 (DE-588)4310554-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Morse-Theorie |0 (DE-588)4197103-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare elliptische Differentialgleichung |0 (DE-588)4310554-3 |D s |
| 689 | 0 | 1 | |a Morse-Theorie |0 (DE-588)4197103-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Pacella, Filomena |e Verfasser |0 (DE-588)119119261X |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-053824-3 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-053743-7 |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications |v Volume 30 |w (DE-604)BV005530011 |9 30 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-031592154 | |
Datensatz im Suchindex
| _version_ | 1819644180637417472 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
V
NOTATION
*
XIII
1
PRELIMINARIES
*
1
1.1
SOBOLEV
SPACES
*
1
1.2
MAXIMUM
PRINCIPLES
*
14
1.2.1
WEAK
MAXIMUM
PRINCIPLE
*
15
1.2.2
STRONG
MAXIMUM
PRINCIPLE
*
20
1.3
COMPACT
SELF-ADJOINT
OPERATORS
*
23
1.4
EIGENVALUES
OF
ELLIPTIC
PROBLEMS
*
29
1.5
SYSTEMS
OF
ELLIPTIC
EQUATIONS
*
43
1.5.1
SPECTRAL
THEORY
FOR
SYMMETRIC
SYSTEMS
*
47
1.5.2
WEAK
MAXIMUM
PRINCIPLE
FOR
COOPERATIVE
SYSTEMS
*
52
1.5.3
COMPARISON
PRINCIPLES
FOR
SEMILINEAR
ELLIPTIC
SYSTEMS
*
55
2
INTRODUCTION
TO
MORSE
THEORY
*
59
2.1
MORSE
THEORY
ON
FINITE
DIMENSIONAL
MANIFOLDS
*
59
2.1.1
INTRODUCTION
-----
59
2.1.2
MORSE
LEMMA
AND
DEFORMATION
THEOREMS
*
62
2.1.3
MORSE
INEQUALITIES
*
68
2.2
INFINITE
DIMENSIONAL
MORSE
THEORY
*
73
2.2.1
CRITICAL
GROUPS
AND
MORSE
LEMMA
*
73
2.2.2
MORSE
INEQUALITIES
*
76
2.2.3
MORSE
INDEX
OF
MOUNTAIN
PASS
CRITICAL
POINTS
*
78
3
MORSE
THEORY
FOR
SEMILINEAR
ELLIPTIC
EQUATIONS
*
83
3.1
INTRODUCTION
*
83
3.2
POSITIVE
SOLUTIONS
OF
DIRICHLET
PROBLEMS
*
86
3.2.1
EXISTENCE
OF
A
POSITIVE
SOLUTION
BY
THE
MOUNTAIN
PASS
THEOREM
*
87
3.2.2
EXISTENCE
OF
A
POSITIVE
SOLUTION
BY
CONSTRAINED
MINIMIZATION
*
89
3.2.3
UNIQUENESS
OF
SOLUTIONS
OF
MORSE
INDEX
ONE
OF
LANE-EMDEN
PROBLEMS
*
91
3.3
SIGN
CHANGING
SOLUTIONS
OF
DIRICHLET
PROBLEMS
*
97
3.3.1
EXISTENCE
OF
A
SOLUTION
WITH
MORSE
INDEX
TWO
BY
CONSTRAINED
MINIMIZATION
*
97
3.3.2
ESTIMATES
OF
MORSE
INDEX
FOR
SYMMETRIC
SIGN
CHANGING
SOLUTIONS:
THE
AUTONOMOUS
CASE
*
104
X
----
1
CONTENTS
3.3.3
ESTIMATES
OF
MORSE
INDEX
FOR
SYMMETRIC
SIGN
CHANGING
SOLUTIONS:
THE
NONAUTONOMOUS
CASE
*
110
4
4.1
MORSE
INDEX
OF
RADIAL
SOLUTIONS
OF
LANE-EMDEN
PROBLEMS
*
121
SPECTRAL
DECOMPOSITION
FOR
THE
LINEARIZED
OPERATOR
AT
A
RADIAL
SOLUTION
*
121
4.2
4.2.1
4.2.2
4.3
ASYMPTOTIC
ANALYSIS
OF
RADIAL
SOLUTIONS
*
128
THE
CASE
N
3
*
128
THE
CASE
N
=
2
*
132
COMPUTATION
OF
THE
MORSE
INDEX
OF
RADIAL
SOLUTIONS
IN
DIMENSION
N
3
*
136
4.4
4.5
COMPUTATION
OF
THE
MORSE
INDEX
IN
DIMENSION
N
=
2
*
143
A
WEIGHTED
EIGENVALUE
PROBLEM
IN
*
147
5
5.1
5.2
5.2.1
5.2.2
5.2.3
5.3
5.3.1
5.3.2
5.3.3
BIFURCATION
FROM
RADIAL
SOLUTIONS
*
155
PRELIMINARIES
*
155
BIFURCATION
WITH
RESPECT
TO
THE
EXPONENT
P
*
158
ASYMPTOTIC
ANALYSIS
OF
THE
RADIAL
SOLUTION
*
158
ASYMPTOTIC
BEHAVIOR
OF
THE
RADIAL
EIGENVALUE
/^(P)
*
160
BIFURCATION
RESULTS
*
165
BIFURCATION
WITH
RESPECT
TO
THE
RADIUS
OF
THE
ANNULUS
*
167
ASYMPTOTIC
ESTIMATES
FOR
THE
RADIAL
SOLUTION
*
167
ASYMPTOTIC
ANALYSIS
OF
THE
EIGENVALUE
&(/?)
*
171
BIFURCATION
RESULTS
*
175
6
MORSE
INDEX
AND
SYMMETRY
FOR
SEMILINEAR
ELLIPTIC
EQUATIONS
IN
BOUNDED
DOMAINS
*
177
6.1
6.1.1
6.1.2
6.1.3
6.2
6.3
SYMMETRY
AND
MONOTONICITY
OF
POSITIVE
SOLUTIONS
*
177
MOVING
PLANES
AND
SYMMETRY
*
177
MONOTONICITY
BY
THE
METHOD
OF
MOVING
PLANES
*
182
COUNTEREXAMPLES
TO
RADIAL SYMMETRY
*
184
FOLIATED
SCHWARZ
SYMMETRY
AND
RELATED
PROPERTIES
*
186
FOLIATED
SCHWARZ
SYMMETRY
OF
LOW
MORSE
INDEX
SOLUTIONS
OF
ELLIPTIC
DIRICHLET
PROBLEMS
*
196
6.3.1
6.3.2
6.4
CONVEX
NONLINEARITIES
*
196
NONLINEARITIES
WITH
A
CONVEX
DERIVATIVE
*
199
SYMMETRY
OF
SOLUTIONS
OF
MIXED
BOUNDARY
VALUE
PROBLEMS
*
205
7
7.1
7.2
7.2.1
MORSE
INDEX
AND
SYMMETRY
FOR
ELLIPTIC
SYSTEMS
IN
BOUNDED
DOMAINS
*
213
MORSE
INDEX
OF
SOLUTIONS
OF
ELLIPTIC
SYSTEMS
*
213
SYMMETRY
RESULTS
*
215
MOVING
AND
ROTATING
PLANES
*
215
CONTENTS
*
XI
7.2.2
7.2.3
7.2.4
7.3
FOLIATED
SCHWARZ
SYMMETRY
*
217
NONLINEARITIES
HAVING
CONVEX
COMPONENTS
*
219
NONLINEARITIES
WITH
CONVEX
DERIVATIVES
*
224
EXAMPLES
*
229
8
8.1
8.2
8.3
SOME
RESULTS
IN
UNBOUNDED
DOMAINS
*
235
MOVING
PLANES
AND
SYMMETRY
IN
UNBOUNDED
DOMAINS
*
235
FOLIATED
SCHWARZ
SYMMETRY
*
239
NONEXISTENCE
AND
CLASSIFICATION
RESULTS
*
242
BIBLIOGRAPHY
*
245
INDEX
*
255
|
| any_adam_object | 1 |
| author | Damascelli, Lucio Pacella, Filomena |
| author_GND | (DE-588)1191192431 (DE-588)119119261X |
| author_facet | Damascelli, Lucio Pacella, Filomena |
| author_role | aut aut |
| author_sort | Damascelli, Lucio |
| author_variant | l d ld f p fp |
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| bvnumber | BV046213305 |
| classification_rvk | SK 560 SK 540 |
| ctrlnum | (OCoLC)1128840839 (DE-599)DNB1175757349 |
| dewey-full | 515.3533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3533 |
| dewey-search | 515.3533 |
| dewey-sort | 3515.3533 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV046213305 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T07:50:38Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110537321 311053732X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031592154 |
| oclc_num | 1128840839 |
| open_access_boolean | |
| owner | DE-634 DE-20 DE-11 |
| owner_facet | DE-634 DE-20 DE-11 |
| physical | XV, 254 Seiten Illustrationen, Diagramme 25 cm, 603 g |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spellingShingle | Damascelli, Lucio Pacella, Filomena Morse index of solutions of nonlinear elliptic equations De Gruyter series in nonlinear analysis and applications Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd Morse-Theorie (DE-588)4197103-6 gnd |
| subject_GND | (DE-588)4310554-3 (DE-588)4197103-6 |
| title | Morse index of solutions of nonlinear elliptic equations |
| title_auth | Morse index of solutions of nonlinear elliptic equations |
| title_exact_search | Morse index of solutions of nonlinear elliptic equations |
| title_full | Morse index of solutions of nonlinear elliptic equations Lucio Damascelli and Filomena Pacella |
| title_fullStr | Morse index of solutions of nonlinear elliptic equations Lucio Damascelli and Filomena Pacella |
| title_full_unstemmed | Morse index of solutions of nonlinear elliptic equations Lucio Damascelli and Filomena Pacella |
| title_short | Morse index of solutions of nonlinear elliptic equations |
| title_sort | morse index of solutions of nonlinear elliptic equations |
| topic | Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd Morse-Theorie (DE-588)4197103-6 gnd |
| topic_facet | Nichtlineare elliptische Differentialgleichung Morse-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031592154&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
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