Methods in nonlinear analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2005
|
| Series: | Springer Monographs in Mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 425-439 Auch als Internetausgabe |
| Physical Description: | IX, 439 S. 235 mm x 155 mm |
| ISBN: | 9783540241331 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | KUNG-CHING CHANG
METHODS IN
NONLINEAR ANALYSIS
4Y SPRINGER
CONTENTS
LINEARIZATIO
N
1
1.1 DIFFERENTIAL CALCULUS IN BANACH SPACES 1
1.1.1 FRECHET DERIVATIVES AND GATEAUX DERIVATIVES 2
1.1.2 NEMYTSCKI OPERATOR 7
1.1.3 HIGH-ORDER DERIVATIVES 9
1.2 IMPLICIT FUNCTION THEOREM AND CONTINUITY METHOD 12
1.2.1 INVERSE FUNCTION THEOREM 12
1.2.2 APPLICATIONS 17
1.2.3 CONTINUITY METHOD 23
1.3 LYAPUNOV-SCHMIDT REDUCTION AND BIFURCATION 30
1.3.1 BIFURCATION 30
1.3.2 LYAPUNOV-SCHMIDT REDUCTION 33
1.3.3 A PERTURBATIO
N PROBLEM 43
1.3.4 GLUING 47
1.3.5 TRANSVERSALITY 49
1.4 HARD IMPLICIT FUNCTION THEOREM 54
1.4.1 THE SMALL DIVISOR PROBLEM 55
1.4.2 NASH-MOSER ITERATION 62
FIXED-POIN
T THEOREM
S
71
2.1 ORDER METHOD 72
2.2 CONVEX FUNCTION AND ITS SUBDIFFERENTIALS 80
2.2.1 CONVEX FUNCTIONS 80
2.2.2 SUBDIFFERENTIALS 84
2.3 CONVEXITY AND COMPACTNESS 87
2.4 NONEXPANSIVE MAPS 104
2.5 MONOTONE MAPPINGS 109
2.6 MAXIMAL MONOTONE MAPPING 120
VIII CONTENTS
3 DEGRE
E THEOR
Y AND APPLICATION
S
127
3.1 THE NOTION OF TOPOLOGICAL DEGREE 128
3.2 FUNDAMENTAL PROPERTIES AND CALCULATIONS OF BROUWER DEGREES . 137
3.3 APPLICATIONS OF BROUWER DEGREE 148
3.3.1 BROUWER FIXED-POINT THEOREM 148
3.3.2 THE BORSUK-ULAM THEOREM AND ITS CONSEQUENCES 148
3.3.3 DEGREES FOR
S
1
EQUIVARIANT MAPPINGS 151
3.3.4 INTERSECTION 153
3.4 LERAY-SCHAUDER DEGREES 155
3.5 THE GLOBAL BIFURCATION 164
3.6 APPLICATIONS 175
3.6.1 DEGREE THEORY ON CLOSED CONVEX SETS 175
3.6.2 POSITIVE SOLUTIONS AND THE SCALING METHOD 180
3.6.3 KREIN-RUTMAN THEORY FOR POSITIVE LINEAR OPERATORS. . . 185
3.6.4 MULTIPLE SOLUTIONS 189
3.6.5 A FREE BOUNDARY PROBLEM 192
3.6.6 BRIDGING 193
3.7 EXTENSIONS 195
3.7.1 SET-VALUED MAPPINGS 195
3.7.2 STRICT SET CONTRACTION MAPPINGS
AND CONDENSING MAPPINGS 198
3.7.3 FREDHOLM MAPPINGS 200
4 MINIMIZATIO
N METHOD
S
205
4.1 VARIATIONAL PRINCIPLES 206
4.1.1 CONSTRAINT PROBLEMS 206
4.1.2 EULER-LAGRANGE EQUATION 209
4.1.3 DUAL VARIATIONAL PRINCIPLE 212
4.2 DIRECT METHOD 216
4.2.1 FUNDAMENTAL PRINCIPLE 216
4.2.2 EXAMPLES 217
4.2.3 THE PRESCRIBING GAUSSIAN CURVATURE PROBLEM
AND THE SCHWARZ SYMMETRIC REARRANGEMENT 223
4.3 QUASI-CONVEXITY 231
4.3.1 WEAK CONTINUITY AND QUASI-CONVEXITY 232
4.3.2 MORREY THEOREM 237
4.3.3 NONLINEAR ELASTICITY 242
4.4 RELAXATION AND YOUNG MEASURE 244
4.4.1 RELAXATIONS 245
4.4.2 YOUNG MEASURE 251
4.5 OTHER FUNCTION SPACES 260
4.5.1 BV SPACE 260
4.5.2 HARDY SPACE AND BMO SPACE 266
4.5.3 COMPENSATION COMPACTNESS 271
4.5.4 APPLICATIONS T
O THE CALCULUS OF VARIATIONS 274
CONTENTS IX
4.6 FREE DISCONTINUOUS PROBLEMS 279
4.6.1 F-CONVERGENCE 279
4.6.2 A PHASE TRANSITION PROBLEM 280
4.6.3 SEGMENTATION AND MUMFORD-SHAH PROBLEM 284
4.7 CONCENTRATION COMPACTNESS 289
4.7.1 CONCENTRATION FUNCTION 289
4.7.2 THE CRITICAL SOBOLEV EXPONENT AND THE BEST CONSTANTS 295
4.8 MINIMAX METHODS 301
4.8.1 EKELAND VARIATIONAL PRINCIPLE 301
4.8.2 MINIMAX PRINCIPLE 303
4.8.3 APPLICATIONS 306
5 TOPOLOGICAL AND VARIATIONAL METHOD
S
315
5.1 MORSE THEORY 317
5.1.1 INTRODUCTION 317
5.1.2 DEFORMATION THEOREM 319
5.1.3 CRITICAL GROUPS 327
5.1.4 GLOBAL THEORY 334
5.1.5 APPLICATIONS 343
5.2 MINIMAX PRINCIPLES (REVISITED) 347
5.2.1 A MINIMAX PRINCIPLE 347
5.2.2 CATEGORY AND LJUSTERNIK-SCHNIRELMANN
MULTIPLICITY THEOREM 349
5.2.3 CAP PRODUCT 354
5.2.4 INDEX THEOREM 358
5.2.5 APPLICATIONS 363
5.3 PERIODIC ORBITS FOR HAMILTONIAN SYSTEM
AND WEINSTEIN CONJECTURE 371
5.3.1 HAMILTONIAN OPERATOR 373
5.3.2 PERIODIC SOLUTIONS 374
5.3.3 WEINSTEIN CONJECTURE 376
5.4 PRESCRIBING GAUSSIAN CURVATURE PROBLEM ON S
2
380
5.4.1 THE CONFORMAL GROUP AND THE BEST CONSTANT 380
5.4.2 THE PALAIS-SMALE SEQUENCE 387
5.4.3 MORSE THEORY FOR THE PRESCRIBING GAUSSIAN CURVATURE
EQUATION ON S
2
389
5.5 CONLEY INDEX THEORY 392
5.5.1 ISOLATED INVARIANT SET 393
5.5.2 INDEX PAIR AND CONLEY INDEX 397
5.5.3 MORSE DECOMPOSITION ON COMPACT INVARIANT SETS
AND ITS EXTENSION 408
NOTE
S
419
REFERENCES
425
|
| any_adam_object | 1 |
| author | Chang, Kung-ching 1936- |
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| bvnumber | BV020824811 |
| callnumber-first | Q - Science |
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| dewey-full | 515.7248 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7248 |
| dewey-search | 515.7248 |
| dewey-sort | 3515.7248 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:20:05Z |
| institution | BVB |
| isbn | 9783540241331 |
| language | English |
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| physical | IX, 439 S. 235 mm x 155 mm |
| publishDate | 2005 |
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| spelling | Chang, Kung-ching 1936- Verfasser (DE-588)133505863 aut Methods in nonlinear analysis Kung-Ching Chang Berlin [u.a.] Springer 2005 IX, 439 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer Monographs in Mathematics Literaturverz. S. 425-439 Auch als Internetausgabe Nichtlineare Analysis Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013830109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chang, Kung-ching 1936- Methods in nonlinear analysis Nichtlineare Analysis Nichtlineare Analysis (DE-588)4177490-5 gnd |
| subject_GND | (DE-588)4177490-5 |
| title | Methods in nonlinear analysis |
| title_auth | Methods in nonlinear analysis |
| title_exact_search | Methods in nonlinear analysis |
| title_full | Methods in nonlinear analysis Kung-Ching Chang |
| title_fullStr | Methods in nonlinear analysis Kung-Ching Chang |
| title_full_unstemmed | Methods in nonlinear analysis Kung-Ching Chang |
| title_short | Methods in nonlinear analysis |
| title_sort | methods in nonlinear analysis |
| topic | Nichtlineare Analysis Nichtlineare Analysis (DE-588)4177490-5 gnd |
| topic_facet | Nichtlineare Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013830109&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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