Nonlinear analysis - theory and methods:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham, Switzerland
Springer
[2019]
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seiten 557-572 |
| Physical Description: | xi, 577 Seiten 23.5 cm x 15.5 cm |
| ISBN: | 3030034291 9783030034290 |
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MARC
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| 245 | 1 | 0 | |a Nonlinear analysis - theory and methods |c Nikolaos Papageorgiou, Vicenţiu Rădulescu, Dušan Repovš |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Sobolev Spaces 1
1 1 Definitions, Density, and Approximation Results 1
1 2 The One-Dimensional Case 13
1 3 Duals of Sobolev Spaces 15
1 4 Absolute Continuity on Lines, the Chain Rule
and Consequences 19
1 5 Trace Theory 26
1 6 The Extension Operator 35
1 7 The Rellich-Kondrachov Theorem 38
1 8 The Poincarf and Poincar6-Wirtinger Inequalities 43
1 9 The Sobolev Embedding Theorem 45
1 10 Capacities Miscellaneous Results 58
1 11 Remarks 66
2 Compact Operators and Operators of Monotone Type 71
2 1 Compact and Completely Continuous Maps 71
2 2 Proper Maps and Gradient Maps 77
2 3 Linear Compact Operators 83
2 4 Spectral Theory of Compact Linear Operators 89
2 5 Multifunctions 100
2 6 Monotone Maps: Definition and Basic Results 113
2 7 The Subdifferential and Duality Maps 118
2 8 Surjectivity and Characterizations of Maximal Monotonicity 130
2 9 Regularizations and Linear Monotone Operators 139
2 10 Operators of Monotone Type 149
2 11 Remarks 160
3 Degree Theories 167
3 1 Brouwer Degree 168
3 2 The Leray-Schauder Degree 188
v
vi Contents
3 3 Degree for Multifunctions 200
3 4 Degree for (S) + -Maps 203
3 5 Degree for Maximal Monotone Perturbation of (5) + -Maps 214
3 6 Degree for Subdifferential Operators 221
3 7 Some Generalizations 235
3 8 Index of a if-Point 253
3 9 Remarks 257
4 Partial Order, Fixed Point Theory, Variational Principles 263
4 1 Cones and Partial Order 264
4 2 Metric Fixed Points 275
4 3 Topological Fixed Points 289
4 4 Order Fixed Points and the Fixed Point Index 303
4 5 Fixed Points for Multifunctions 314
4 6 Abstract Variational Principles 319
4 7 Young Measures 340
4 8 Remarks 356
5 Critical Point Theory 361
5 1 Pseudogradients and Compactness Conditions 363
5 2 Critical Points via Minimization—The Direct Method 373
5 3 Deformation Theorems 379
5 4 Minimax Theorems 397
5 5 Critical Points Under Constraints 420
5 6 Critical Points Under Symmetries 427
5 7 The Structure of the Critical Set 444
5 8 Remarks 451
6 Morse Theory and Critical Groups 457
6 1 Elements of Algebraic Topology 458
6 2 Critical Groups, Morse Relations 477
6 3 Continuity and Homotopy Invariance of Critical Groups 501
6 4 Extended Gromoll-Meyer Theory 506
6 5 Local Extrema and Critical Points of Mountain Pass Type 526
6 6 Computation of Critical Groups 530
6 7 Existence and Multiplicity of Critical Points 545
6 8 Remarks 553
References 557
|
| adam_txt |
Contents
1 Sobolev Spaces 1
1 1 Definitions, Density, and Approximation Results 1
1 2 The One-Dimensional Case 13
1 3 Duals of Sobolev Spaces 15
1 4 Absolute Continuity on Lines, the Chain Rule
and Consequences 19
1 5 Trace Theory 26
1 6 The Extension Operator 35
1 7 The Rellich-Kondrachov Theorem 38
1 8 The Poincarf and Poincar6-Wirtinger Inequalities 43
1 9 The Sobolev Embedding Theorem 45
1 10 Capacities Miscellaneous Results 58
1 11 Remarks 66
2 Compact Operators and Operators of Monotone Type 71
2 1 Compact and Completely Continuous Maps 71
2 2 Proper Maps and Gradient Maps 77
2 3 Linear Compact Operators 83
2 4 Spectral Theory of Compact Linear Operators 89
2 5 Multifunctions 100
2 6 Monotone Maps: Definition and Basic Results 113
2 7 The Subdifferential and Duality Maps 118
2 8 Surjectivity and Characterizations of Maximal Monotonicity 130
2 9 Regularizations and Linear Monotone Operators 139
2 10 Operators of Monotone Type 149
2 11 Remarks 160
3 Degree Theories 167
3 1 Brouwer Degree 168
3 2 The Leray-Schauder Degree 188
v
vi Contents
3 3 Degree for Multifunctions 200
3 4 Degree for (S) + -Maps 203
3 5 Degree for Maximal Monotone Perturbation of (5) + -Maps 214
3 6 Degree for Subdifferential Operators 221
3 7 Some Generalizations 235
3 8 Index of a if-Point 253
3 9 Remarks 257
4 Partial Order, Fixed Point Theory, Variational Principles 263
4 1 Cones and Partial Order 264
4 2 Metric Fixed Points 275
4 3 Topological Fixed Points 289
4 4 Order Fixed Points and the Fixed Point Index 303
4 5 Fixed Points for Multifunctions 314
4 6 Abstract Variational Principles 319
4 7 Young Measures 340
4 8 Remarks 356
5 Critical Point Theory 361
5 1 Pseudogradients and Compactness Conditions 363
5 2 Critical Points via Minimization—The Direct Method 373
5 3 Deformation Theorems 379
5 4 Minimax Theorems 397
5 5 Critical Points Under Constraints 420
5 6 Critical Points Under Symmetries 427
5 7 The Structure of the Critical Set 444
5 8 Remarks 451
6 Morse Theory and Critical Groups 457
6 1 Elements of Algebraic Topology 458
6 2 Critical Groups, Morse Relations 477
6 3 Continuity and Homotopy Invariance of Critical Groups 501
6 4 Extended Gromoll-Meyer Theory 506
6 5 Local Extrema and Critical Points of Mountain Pass Type 526
6 6 Computation of Critical Groups 530
6 7 Existence and Multiplicity of Critical Points 545
6 8 Remarks 553
References 557 |
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| author | Papageōrgiu, Nikolaos 1958- Rădulescu, Vicenţiu D. 1958- Repovš, Dušan 1954- |
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| author_facet | Papageōrgiu, Nikolaos 1958- Rădulescu, Vicenţiu D. 1958- Repovš, Dušan 1954- |
| author_role | aut aut aut |
| author_sort | Papageōrgiu, Nikolaos 1958- |
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| ctrlnum | (OCoLC)1105060973 (DE-599)DNB1167872339 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:45:48Z |
| indexdate | 2024-07-10T09:17:44Z |
| institution | BVB |
| institution_GND | (DE-588)1064344704 |
| isbn | 3030034291 9783030034290 |
| language | English |
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| physical | xi, 577 Seiten 23.5 cm x 15.5 cm |
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| spelling | Papageōrgiu, Nikolaos 1958- Verfasser (DE-588)137051085 aut Nonlinear analysis - theory and methods Nikolaos Papageorgiou, Vicenţiu Rădulescu, Dušan Repovš Cham, Switzerland Springer [2019] © 2019 xi, 577 Seiten 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverzeichnis: Seiten 557-572 Differentialoperator (DE-588)4012251-7 gnd rswk-swf Nichtlineares Eigenwertproblem (DE-588)4459707-1 gnd rswk-swf Nichtlineares Eigenwertproblem (DE-588)4459707-1 s Differentialoperator (DE-588)4012251-7 s DE-604 Rădulescu, Vicenţiu D. 1958- Verfasser (DE-588)138708924 aut Repovš, Dušan 1954- Verfasser (DE-588)1124413308 aut Springer International Publishing (DE-588)1064344704 pbl Erscheint auch als Online-Ausgabe 978-3-030-03430-6 10.1007/978-3-030-03430-6 X: MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=cf6543bd61e04b78b44527f0778c1222&prov=M&dok_var=1&dok_ext=htm 2018-10-05 Verlag Inhaltstext B:ZBM https://zbmath.org/?q=an:1414.46003 2021-04-12 Verlag Zentralblatt MATH Inhaltstext HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033016642&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Papageōrgiu, Nikolaos 1958- Rădulescu, Vicenţiu D. 1958- Repovš, Dušan 1954- Nonlinear analysis - theory and methods Differentialoperator (DE-588)4012251-7 gnd Nichtlineares Eigenwertproblem (DE-588)4459707-1 gnd |
| subject_GND | (DE-588)4012251-7 (DE-588)4459707-1 |
| title | Nonlinear analysis - theory and methods |
| title_auth | Nonlinear analysis - theory and methods |
| title_exact_search | Nonlinear analysis - theory and methods |
| title_exact_search_txtP | Nonlinear analysis - theory and methods |
| title_full | Nonlinear analysis - theory and methods Nikolaos Papageorgiou, Vicenţiu Rădulescu, Dušan Repovš |
| title_fullStr | Nonlinear analysis - theory and methods Nikolaos Papageorgiou, Vicenţiu Rădulescu, Dušan Repovš |
| title_full_unstemmed | Nonlinear analysis - theory and methods Nikolaos Papageorgiou, Vicenţiu Rădulescu, Dušan Repovš |
| title_short | Nonlinear analysis - theory and methods |
| title_sort | nonlinear analysis theory and methods |
| topic | Differentialoperator (DE-588)4012251-7 gnd Nichtlineares Eigenwertproblem (DE-588)4459707-1 gnd |
| topic_facet | Differentialoperator Nichtlineares Eigenwertproblem |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=cf6543bd61e04b78b44527f0778c1222&prov=M&dok_var=1&dok_ext=htm https://zbmath.org/?q=an:1414.46003 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033016642&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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