Perturbation methods and semilinear elliptic problems on R n:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2006
|
| Schriftenreihe: | Progress in mathematics
240 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017479669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | IX, 183 S. graph. Darst. 24 cm |
| ISBN: | 9783764373214 3764373210 |
Internformat
MARC
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| 245 | 1 | 0 | |a Perturbation methods and semilinear elliptic problems on R n |c Antonio Ambrosetti ; Andrea Malchiodi |
| 246 | 1 | 3 | |a Perturbation methods and semilinear elliptic problems on R[n] |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2006 | |
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Datensatz im Suchindex
| _version_ | 1819322539061542912 |
|---|---|
| adam_text | Contents
Foreword xi
Notation xii
1 Examples and Motivations
1.1 Elliptic equations on Mn 1
1.1.1 The subcritical case 2
1.1.2 The critical case: the Scalar Curvature Problem 3
1.2 Bifurcation from the essential spectrum 5
1.3 Semiclassical standing waves of NLS 6
1.4 Other problems with concentration 8
1.4.1 Neumann singularly perturbed problems 8
1.4.2 Concentration on spheres for radial problems 9
1.5 The abstract setting 10
2 Pertubation in Critical Point Theory
2.1 A review on critical point theory 13
2.2 Critical points for a class of perturbed functionals, I 19
2.2.1 A finite-dimensional reduction:
the Lyapunov-Schmidt method revisited 20
2.2.2 Existence of critical points 22
2.2.3 Other existence results 24
2.2.4 A degenerate case 26
2.2.5 A further existence result 27
2.2.6 Morse index of the critical points of Ie 29
2.3 Critical points for a class of perturbed functionals, II 29
2.4 A more general case 33
viii Contents
3 Bifurcation from the Essential Spectrum
3.1 A first bifurcation result 35
3.1.1 The unperturbed problem 36
3.1.2 Study of G 37
3.2 A second bifurcation result 39
3.3 A problem arising in nonlinear optics 41
4 Elliptic Problems on Mn with Subcritical Growth
4.1 The abstract setting 45
4.2 Study of the Ker[/£(^)] 47
4.3 A first existence result 50
4.4 Another existence result 52
5 Elliptic Problems with Critical Exponent
5.1 The unperturbed problem 59
5.2 On the Yamabe-like equation 62
5.2.1 Some auxiliary lemmas 63
5.2.2 Proof of Theorem 5.3 66
5.2.3 The radial case 67
5.3 Further existence results 68
6 The Yamabe Problem
6.1 Basic notions and facts 73
6.1.1 The Yamabe problem 74
6.2 Some geometric preliminaries 76
6.3 First multiplicity results 80
6.3.1 Expansions of the functionals 80
6.3.2 The finite-dimensional functional 82
6.3.3 Proof of Theorem 6.2 86
6.4 Existence of infinitely-many solutions 88
6.4.1 Proof of Theorem 6.3 completed 90
6.5 Appendix 92
7 Other Problems in Conformal Geometry
7.1 Prescribing the scalar curvature of the sphere 101
7.2 Problems with symmetry 105
7.2.1 The perturbative case 105
7.3 Prescribing Scalar and Mean Curvature
on manifolds with boundary 109
7.3.1 The Yamabe-like problem 109
7.3.2 The Scalar Curvature Problem with
boundary conditions Ill
Contents ix
8 Nonlinear Schrodinger Equations
8.1 Necessary conditions for existence of spikes 115
8.2 Spikes at non-degenerate critical points of V 117
8.3 The general case: Preliminaries 121
8.4 A modified abstract approach 123
8.5 Study of the reduced functional 131
9 Singularly Perturbed Neumann Problems
9.1 Preliminaries 135
9.2 Construction of approximate solutions 138
9.3 The abstract setting 143
9.4 Proof of Theorem 9.1 146
10 Concentration at Spheres for Radial Problems
10.1 Concentration at spheres for radial NLS 151
10.2 The finite-dimensional reduction 153
10.2.1 Some preliminary estimates 154
10.2.2 Solving PI £(z + w) = 0 156
10.3 Proof of Theorem 10.1 159
10.3.1 Proof of Theorem 10.1 completed 160
10.4 Other results 160
10.5 Concentration at spheres for (NE) 162
10.5.1 The finite-dimensional reduction 163
10.5.2 Proof of Theorem 10.12 166
10.5.3 Further results 171
Bibliography 173
Index 181
|
| any_adam_object | 1 |
| author | Ambrosetti, Antonio 1944-2020 Malchiodi, Andrea |
| author_GND | (DE-588)111667070 (DE-588)130563021 |
| author_facet | Ambrosetti, Antonio 1944-2020 Malchiodi, Andrea |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV023837557 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:35:06Z |
| institution | BVB |
| isbn | 9783764373214 3764373210 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017479669 |
| oclc_num | 318296810 |
| open_access_boolean | |
| owner | DE-634 DE-384 DE-19 DE-BY-UBM |
| owner_facet | DE-634 DE-384 DE-19 DE-BY-UBM |
| physical | IX, 183 S. graph. Darst. 24 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spellingShingle | Ambrosetti, Antonio 1944-2020 Malchiodi, Andrea Perturbation methods and semilinear elliptic problems on R n Progress in mathematics Störungstheorie (DE-588)4128420-3 gnd Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4225683-5 |
| title | Perturbation methods and semilinear elliptic problems on R n |
| title_alt | Perturbation methods and semilinear elliptic problems on R[n] |
| title_auth | Perturbation methods and semilinear elliptic problems on R n |
| title_exact_search | Perturbation methods and semilinear elliptic problems on R n |
| title_full | Perturbation methods and semilinear elliptic problems on R n Antonio Ambrosetti ; Andrea Malchiodi |
| title_fullStr | Perturbation methods and semilinear elliptic problems on R n Antonio Ambrosetti ; Andrea Malchiodi |
| title_full_unstemmed | Perturbation methods and semilinear elliptic problems on R n Antonio Ambrosetti ; Andrea Malchiodi |
| title_short | Perturbation methods and semilinear elliptic problems on R n |
| title_sort | perturbation methods and semilinear elliptic problems on r n |
| topic | Störungstheorie (DE-588)4128420-3 gnd Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd |
| topic_facet | Störungstheorie Semilineare elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017479669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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