Linking methods in critical point theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
1999
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Bibliogr. S. 269 - 292 |
| Beschreibung: | XVI, 294 S. |
| ISBN: | 3764340959 0817640959 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804127069353803776 |
|---|---|
| adam_text | Contents
FOREWORD ix
PREFACE xi
1 CRITICAL POINT THEORY 1
1.1 Introduction 1
1.2 Other Geometries 5
1.3 Semilinear Boundary Value Problems 7
1.4 The Critical Point Alternative 9
1.5 The Mountain Cliff Theorem 9
1.6 Estimates on Eigenspaces 11
1.7 Asymptotic Limits 13
1.8 Types of Resonance 14
1.9 Multiple Solutions 16
1.10 Eigenvalues 17
2 LINKING 21
2.1 The Basic Concept 21
2.2 The Flow 23
2.3 Weaker Conditions 27
2.4 Another Form 30
2.5 Some Consequences 33
2.6 Examples of Linking 36
2.7 Critical Sequences 42
2.8 The Compact Case 45
2.9 A Sandwich Theorem 48
2.10 Appendix I: Pseudo Gradients 51
2.11 Appendix II: Differential Equations 52
v
vi CONTENTS
3 SEMILINEAR BOUNDARY VALUE PROBLEMS 55
3.1 Introduction 55
3.2 Mountain Pass Geometry 58
3.3 Finding a Critical Sequence 62
3.4 Obtaining a Solution 63
3.5 Solving the Problem 66
3.6 Resonance 68
3.7 Appendix I: The Sobolev Inequality 72
4 ALTERNATIVE METHODS 73
4.1 Introduction 73
4.2 The Saddle Point Alternative 74
4.3 An Alternate Form 78
4.4 Some Corollaries 81
4.5 An Application 85
4.6 Superlinear Problems 91
4.7 Some Modifications 95
5 BOUNDED SADDLE POINT METHODS 99
5.1 Introduction 99
5.2 A Bounded Mountain Pass Lemma 100
5.3 The Mountain Pass Alternative 105
5.4 A Compactness Condition 107
5.5 Dual Situations 110
5.6 Combined Results 113
5.7 Nonlinear Eigenvalues 117
5.8 Double Resonance 121
5.9 Appendix I: Generalized Pseudo Gradients 128
6 ESTIMATES ON SUBSPACES 131
6.1 Introduction 131
6.2 Some Important Quantities 132
6.3 The Estimates 137
6.4 Nontrivial Solutions 140
6.5 A Variation 142
7 THE FUCIK SPECTRUM 145
7.1 Introduction 145
7.2 Jumping Nonlinearities 146
7.3 Quantities Related to the Fuci k Spectrum 148
CONTENTS vii
7.4 Applications 163
8 RESONANCE 167
8.1 Introduction 167
8.2 More on Double Resonance 168
8.3 Resonance Involving Many Eigenvalues 171
8.4 Landesman Lazer Resonance 176
8.5 Equal Limits at Infinity 185
8.6 Nonvanishing Solutions 192
8.7 Unequal Limits at Infinity 197
9 BOUNDARY CONDITIONS 205
9.1 Introduction 205
9.2 Bounded Linking 205
9.3 Reverse Boundary Conditions 209
9.4 An Application 212
9.5 Sufficient Conditions 215
10 MULTIPLE SOLUTIONS 219
10.1 Introduction 219
10.2 The Abstract Theory 219
10.3 Some Applications 222
10.4 Additional Solutions 227
11 NONLINEAR EIGENVALUES 229
11.1 Introduction 229
11.2 The Hampwile Theorem 230
11.3 Applications 236
12 STRONG RESONANCE 239
12.1 Introduction 239
12.2 Simple Solutions 240
12.3 A Different Approach 243
12.4 Resonance at the First Eigenvalue 246
12.5 Additional Solutions 251
13 NOTES, REMARKS and REFERENCES 255
BIBLIOGRAPHY 269
INDEX 293
|
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| id | DE-604.BV012430931 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:27:29Z |
| institution | BVB |
| isbn | 3764340959 0817640959 |
| language | German |
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| physical | XVI, 294 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Schechter, Martin 1930- Verfasser (DE-588)1042649022 aut Linking methods in critical point theory Martin Schechter Boston ; Basel ; Berlin Birkhäuser 1999 XVI, 294 S. txt rdacontent n rdamedia nc rdacarrier Bibliogr. S. 269 - 292 Points critiques, Théorie des (Analyse mathématique) Problèmes aux limites Boundary value problems Critical point theory (Mathematical analysis) Kritischer Punkt Mathematik (DE-588)4207169-0 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Kritischer Punkt Mathematik (DE-588)4207169-0 s DE-604 Randwertproblem (DE-588)4048395-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schechter, Martin 1930- Linking methods in critical point theory Points critiques, Théorie des (Analyse mathématique) Problèmes aux limites Boundary value problems Critical point theory (Mathematical analysis) Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4207169-0 (DE-588)4048395-2 |
| title | Linking methods in critical point theory |
| title_auth | Linking methods in critical point theory |
| title_exact_search | Linking methods in critical point theory |
| title_full | Linking methods in critical point theory Martin Schechter |
| title_fullStr | Linking methods in critical point theory Martin Schechter |
| title_full_unstemmed | Linking methods in critical point theory Martin Schechter |
| title_short | Linking methods in critical point theory |
| title_sort | linking methods in critical point theory |
| topic | Points critiques, Théorie des (Analyse mathématique) Problèmes aux limites Boundary value problems Critical point theory (Mathematical analysis) Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Points critiques, Théorie des (Analyse mathématique) Problèmes aux limites Boundary value problems Critical point theory (Mathematical analysis) Kritischer Punkt Mathematik Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schechtermartin linkingmethodsincriticalpointtheory |