Topics in critical point theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
2013
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
198 |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | "This book introduces the reader to powerful methods of critical point theory and details successful contemporary approaches to many problems, some of which had proved resistant to attack by older methods. Topics covered include Morse theory, critical groups, the minimax principle, various notions of linking, jumping nonlinearities and the Fučík spectrum in an abstract setting, sandwich pairs and the cohomological index. Applications to semilinear elliptic boundary value problems, p-Laplacian problems and anisotropic systems are given. Written for graduate students and research scientists, the book includes numerous examples and presents more recent developments in the subject to bring the reader up to date with the latest research"-- Provided by publisher. -- "Critical point theory has become a very powerful tool for solving many problems. The theory has enjoyed significant development over the last several years. The impetus for this development is the fact that many new problems could not be solved by the older theory. In this book we present more recent developments in the subject that do not seem to be covered elsewhere, including some results of the authors dealing with nonstandard linking geometries and sandwich pairs"-- Provided by publisher. Includes bibliographical references and index |
| Physical Description: | XI, 157 S. |
| ISBN: | 9781107029668 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Topics in critical point theory
Autor: Perera, Kanishka
Jahr: 2012
Contents
Preface page ix
Morse theory 1
1.1 Introduction 1
1.2 Compactness conditions 9
1.3 Deformation lemmas 9
1.4 Critical groups 18
1.5 Minimizers 22
1.6 Nontrivial critical points 22
1.7 Mountain pass points 24
1.8 Three critical points theorem 24
1.9 Generalized local linking 25
1.10 p-Laplacian 25
Linking 30
2.1 Introduction 30
2.2 Minimax principle 30
2.3 Homotopical linking 31
2.4 Homological linking 33
2.5 Schechter and Tintarev s notion of linking 36
2.6 Pairs of critical points with nontrivial critical groups 40
2.7 Nonstandard geometries 42
Applications to semilinear problems 47
3.1 Introduction 47
3.2 Local nature of critical groups 48
3.3 Critical groups at zero 50
vu
viii Contents
3.4 Asymptotically linear problems 57
3.5 Problems with concave nonlinearities 63
Fucik spectrum 67
4.1 Introduction 67
4.2 Examples 69
4.3 Preliminaries on Operators 72
4.4 Variational formulation 74
4.5 Some estimates 75
4.6 Convexity and concavity 77
4.7 Minimal and maximal curves 78
4.8 Nullmanifold 93
4.9 Type II regions 100
4.10 Simple eigenvalues 101
4.11 Critical groups 101
Jumping nonlinearities 107
5.1 Introduction 107
5.2 Compactness 109
5.3 Critical groups at intinity 110
5.4 Solvability 115
5.5 Critical groups at zero 116
5.6 Nonlinearities crossing the Fucfk spectrum 122
Sandwich pairs 125
6.1 Introduction 125
6.2 Flows 125
6.3 Cohomological index 126
6.4 Semilinear problems 131
6.5 p-Laplacian problems 133
6.6 Anisotropie Systems 136
Appendix Sobolev spaces 143
A.l Sobolev inequality 143
A.2 Sobolev Spaces 144
Bibliography 147
Index 156
|
| any_adam_object | 1 |
| author | Perera, Kanishka 1969- Schechter, Martin 1930- |
| author_GND | (DE-588)14150627X (DE-588)1042649022 |
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| ctrlnum | (OCoLC)819620875 (DE-599)BVBBV040636101 |
| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040636101 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:27:58Z |
| institution | BVB |
| isbn | 9781107029668 |
| language | English |
| lccn | 2012025065 |
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| physical | XI, 157 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
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| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Perera, Kanishka 1969- Verfasser (DE-588)14150627X aut Topics in critical point theory Kanishka Perera ; Martin Schechter 1. publ. 2013 XI, 157 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 198 "This book introduces the reader to powerful methods of critical point theory and details successful contemporary approaches to many problems, some of which had proved resistant to attack by older methods. Topics covered include Morse theory, critical groups, the minimax principle, various notions of linking, jumping nonlinearities and the Fučík spectrum in an abstract setting, sandwich pairs and the cohomological index. Applications to semilinear elliptic boundary value problems, p-Laplacian problems and anisotropic systems are given. Written for graduate students and research scientists, the book includes numerous examples and presents more recent developments in the subject to bring the reader up to date with the latest research"-- Provided by publisher. -- "Critical point theory has become a very powerful tool for solving many problems. The theory has enjoyed significant development over the last several years. The impetus for this development is the fact that many new problems could not be solved by the older theory. In this book we present more recent developments in the subject that do not seem to be covered elsewhere, including some results of the authors dealing with nonstandard linking geometries and sandwich pairs"-- Provided by publisher. Includes bibliographical references and index Fixed point theory MATHEMATICS / Mathematical Analysis bisacsh Kritischer Punkt Mathematik (DE-588)4207169-0 gnd rswk-swf Kritischer Punkt Mathematik (DE-588)4207169-0 s DE-604 Schechter, Martin 1930- Verfasser (DE-588)1042649022 aut Cambridge tracts in mathematics 198 (DE-604)BV000000001 198 http://www.loc.gov/catdir/enhancements/fy1211/2012025065-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy1211/2012025065-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy1211/2012025065-t.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025463252&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Perera, Kanishka 1969- Schechter, Martin 1930- Topics in critical point theory Cambridge tracts in mathematics Fixed point theory MATHEMATICS / Mathematical Analysis bisacsh Kritischer Punkt Mathematik (DE-588)4207169-0 gnd |
| subject_GND | (DE-588)4207169-0 |
| title | Topics in critical point theory |
| title_auth | Topics in critical point theory |
| title_exact_search | Topics in critical point theory |
| title_full | Topics in critical point theory Kanishka Perera ; Martin Schechter |
| title_fullStr | Topics in critical point theory Kanishka Perera ; Martin Schechter |
| title_full_unstemmed | Topics in critical point theory Kanishka Perera ; Martin Schechter |
| title_short | Topics in critical point theory |
| title_sort | topics in critical point theory |
| topic | Fixed point theory MATHEMATICS / Mathematical Analysis bisacsh Kritischer Punkt Mathematik (DE-588)4207169-0 gnd |
| topic_facet | Fixed point theory MATHEMATICS / Mathematical Analysis Kritischer Punkt Mathematik |
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