Infinite dimensional Morse theory and multiple solution problems
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1993
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| Schriftenreihe: | Progress in nonlinear differential equations and their applications
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Infinite dimensional Morse theory and multiple solution problems |c Kung-ching Chang |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1993 | |
| 300 | |a X, 312 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 6 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 650 | 7 | |a Morse theorie |2 gtt | |
| 650 | 7 | |a Morse, théorie de |2 ram | |
| 650 | 4 | |a calcul variation | |
| 650 | 4 | |a théorie Morse | |
| 650 | 4 | |a Morse theory | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 576f 2001 A 10350 |
|---|---|
| DE-BY-TUM_katkey | 586576 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010683286 |
| _version_ | 1820813023072223232 |
| adam_text | Table of Contents
Preface vii
Introduction ix
Chapter I: Infinite Dimensional Morse Theory
1. A Review of Algebraic Topology 1
2. A Review of the Banach Finsler Manifold 14
3. Pseudo Gradient Vector Field and the Deformation Theorems . 19
4. Critical Groups and Morse Type Numbers 32
5. Gromoll Meyer Theory 43
6. Extensions of Morse Theory 54
6.1. Morse Theory Under General Boundary Conditions . . 55
6.2. Morse Theory on a Locally Convex Closed Set 60
7. Equivariant Morse Theory 65
7.1. Preliminaries 66
7.2. Equivariant Deformation 67
7.3. The Splitting Theorem and the Handle Body Theorem
for Critical Manifolds 69
7.4. G Cohomology and G Critical Groups 74
Chapter II: Critical Point Theory.
1. Topological Link 83
2. Morse Indices of Minimax Critical Points 92
2.1. Link 92
2.2. Genus and Cogenus 96
3. Connections with Other Theories 99
3.1. Degree theory 99
3.2. Ljusternik Schnirelman Theory 105
3.3. Relative Category 109
4. Invariant Functionals Ill
5. Some Abstract Critical Point Theorems 121
6. Perturbation Theory 131
6.1. Perturbation on Critical Manifolds 131
6.2. Uhlenbeck s Perturbation Method 136
Chapter III: Applications to Semilinear Elliptic Boundary Value Problems.
1. Preliminaries 140
2. Superlinear Problems 144
3. Asymptotically Linear Problems 153
vi Infinite Dimensional Morse Theory
3.1. Nonresonance and Resonance with the Landesman Lazer
Condition 153
3.2. Strong Resonance 156
3.3. A Bifurcation Problem 161
3.4. Jumping Nonlinearities 164
3.5. Other Examples 169
4. Bounded Nonlinearities 172
4.1. Functionals Bounded From Below 172
4.2. Oscillating Nonlinearity 173
4.3. Even Functionals 176
4.4. Variational Inequalities 177
Chapter IV: Multiple Periodic Solutions of Hamiltonian Systems
1. Asymptotically Linear Systems 182
2. Reductions and Periodic Nonlinearities 188
2.1. Saddle Point Reduction 188
2.2. A Multiple Solution Theorem 195
2.3. Periodic Nonlinearity 198
3. Singular Potentials 203
4. The Multiple Pendulum Equation 209
5. Some Results on Arnold Conjectures 215
5.1. Conjectures 215
5.2. The Fixed Point Conjecture on (T2 , u 0) 218
5.3. Lagrange Intersections for (CP ,RPn) 220
Chapter V: Applications to Harmonic Maps and Minimal Surfaces
1. Harmonic Maps and the Heat Flow 229
2. The Morse Inequalities 246
3. Morse Decomposition 250
4. The Existence and Multiplicity for Harmonic Maps 257
5. The Plateau Problem for Minimal Surfaces 260
Appendix: Witten s Proof of the Morse Inequalities
1. A Review of Hodge Theory 274
2. The Witten Complex 282
3. Weak Morse Inequalities 287
4. Morse Inequalities 295
References 298
Index of Notation 310
Index 311
|
| any_adam_object | 1 |
| author | Chang, Kung-ching 1936- |
| author_GND | (DE-588)133505863 |
| author_facet | Chang, Kung-ching 1936- |
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| ctrlnum | (OCoLC)23383893 (DE-599)BVBBV007039414 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-12-23T12:18:52Z |
| institution | BVB |
| isbn | 0817634517 3764334517 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004466301 |
| oclc_num | 23383893 |
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| physical | X, 312 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spellingShingle | Chang, Kung-ching 1936- Infinite dimensional Morse theory and multiple solution problems Progress in nonlinear differential equations and their applications EDP non linéaire Morse theorie gtt Morse, théorie de ram calcul variation théorie Morse Morse theory Randwertproblem (DE-588)4048395-2 gnd Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Lösung Mathematik (DE-588)4120678-2 gnd Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd Morse-Theorie (DE-588)4197103-6 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4207169-0 (DE-588)4120678-2 (DE-588)4225683-5 (DE-588)4139943-2 (DE-588)4197103-6 |
| title | Infinite dimensional Morse theory and multiple solution problems |
| title_auth | Infinite dimensional Morse theory and multiple solution problems |
| title_exact_search | Infinite dimensional Morse theory and multiple solution problems |
| title_full | Infinite dimensional Morse theory and multiple solution problems Kung-ching Chang |
| title_fullStr | Infinite dimensional Morse theory and multiple solution problems Kung-ching Chang |
| title_full_unstemmed | Infinite dimensional Morse theory and multiple solution problems Kung-ching Chang |
| title_short | Infinite dimensional Morse theory and multiple solution problems |
| title_sort | infinite dimensional morse theory and multiple solution problems |
| topic | EDP non linéaire Morse theorie gtt Morse, théorie de ram calcul variation théorie Morse Morse theory Randwertproblem (DE-588)4048395-2 gnd Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Lösung Mathematik (DE-588)4120678-2 gnd Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd Morse-Theorie (DE-588)4197103-6 gnd |
| topic_facet | EDP non linéaire Morse theorie Morse, théorie de calcul variation théorie Morse Morse theory Randwertproblem Kritischer Punkt Mathematik Lösung Mathematik Semilineare elliptische Differentialgleichung Hamiltonsches System Morse-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004466301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
| work_keys_str_mv | AT changkungching infinitedimensionalmorsetheoryandmultiplesolutionproblems |