Duality and perturbation methods in critical point theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1993
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
107 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 258 S. graph. Darst. |
| ISBN: | 0521440254 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV008243112 | ||
| 003 | DE-604 | ||
| 005 | 19940413 | ||
| 007 | t | ||
| 008 | 930929s1993 d||| |||| 00||| eng d | ||
| 020 | |a 0521440254 |9 0-521-44025-4 | ||
| 035 | |a (OCoLC)246327701 | ||
| 035 | |a (DE-599)BVBBV008243112 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91 |a DE-739 |a DE-20 |a DE-703 |a DE-19 |a DE-634 |a DE-11 |a DE-188 | ||
| 084 | |a SK 350 |0 (DE-625)143233: |2 rvk | ||
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a SK 660 |0 (DE-625)143251: |2 rvk | ||
| 084 | |a MAT 490f |2 stub | ||
| 084 | |a MAT 576f |2 stub | ||
| 084 | |a MAT 418f |2 stub | ||
| 100 | 1 | |a Ghoussoub, Nassif |d 1953- |e Verfasser |0 (DE-588)137025246 |4 aut | |
| 245 | 1 | 0 | |a Duality and perturbation methods in critical point theory |c Nassif Ghoussoub |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Press |c 1993 | |
| 300 | |a XVIII, 258 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics |v 107 | |
| 650 | 0 | 7 | |a Störungstheorie |0 (DE-588)4128420-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kritischer Punkt |g Mathematik |0 (DE-588)4207169-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dualitätstheorie |0 (DE-588)4150801-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kritischer Punkt |g Mathematik |0 (DE-588)4207169-0 |D s |
| 689 | 0 | 1 | |a Dualitätstheorie |0 (DE-588)4150801-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Kritischer Punkt |g Mathematik |0 (DE-588)4207169-0 |D s |
| 689 | 1 | 1 | |a Störungstheorie |0 (DE-588)4128420-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Cambridge tracts in mathematics |v 107 |w (DE-604)BV000000001 |9 107 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005442309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005442309 | ||
Datensatz im Suchindex
| _version_ | 1804122633092988928 |
|---|---|
| adam_text | CONTENTS
Preface xi
Introduction xiii
Chapter 1. Lipschitz and Smooth Perturbed
Minimization Principles 1
1.1 Ekeland s variational principle 1
1.2 Constrained minimization and global critical points 5
1.3 A non homogeneous elliptic equation involving
the critical Sobolev exponent 8
1.4 Weak sub solutions and super solutions 12
1.5 A minimization principle with quadratic perturbations 14
1.6 The Hartree Fock equations for Coulomb systems 17
1.7 A general perturbed minimization principle 21
1.8 Perturbed minimization and differentiability 26
1.9 Infinite dimensional Hamilton Jacobi equations 29
Notes and Comments 33
Chapter 2. Linear and Plurisubharmonic Perturbed
Minimization Principles 34
2.1 A minimization principle with linear perturbations 34
2.2 Weak* H^ subsets of dual Banach spaces 35
2.3 Generic results for non homogeneous elliptic equations 39
2.4 Analytic martingales and optimization in IP (0 p 1) 41
2.5 A variational characterization of the plurisubharmonic
envelope of a function 43
viii Contents
2.6 A plurisubharmonically perturbed minimization principle 45
Notes and Comments 50
Chapter 3. The Classical Min Max Theorem 52
3.1 Homotopy stable families 52
3.2 The basic deformation lemma for C1 manifolds 55
3.3 The standard (PS) condition and a subcritical elliptic
boundary value problem 58
3.4 The (PS) condition along a min maxing sequence of sets
and a resonant boundary value problem 61
Notes and Comments 66
Chapter 4. A Strong Form of the Min Max Principle 67
4.1 Duality and the location of critical points 67
4.2 The (PS) condition around a dual set
and a relaxed boundary condition 72
4.3 The forced pendulum 74
4.4 The structure of the critical set and the existence
of good paths 76
4.5 Multiplicity results of Ljusternik Schnirehnann type 77
4.6 Functionals with a common critical level and multiplicity
of non radial solutions on the annulus 80
Notes and Comments 89
Chapter 5. Relaxed Boundary Conditions in the
Presence of a Dual Set 90
5.1 Another relaxation of the boundary condition 90
5.2 The relaxed mountain pass and saddle point theorems 95
5.3 The forced double pendulum 97
5.4 A relaxed boundary condition in the presence of linking 104
5.5 Second order systems 106
5.6 Critical points in the presence of splitting 108
5.7 Multiple solutions for a boundary value problem 110
5.8 Multiple solutions for a nonlinear eigenvalue problem 111
Notes and Comments 113
Chapter 6. The Critical Set in the Mountain Pass
Theorem 114
6.1 Saddle points of mountain pass type 115
6.2 A theorem of G. Fang 120
Contents ix
6.3 A bifurcation problem 126
Notes and Comments 127
Chapter 7. Group Actions and Multiplicity
of Critical Points 128
7.1 The equivariant min max principles 128
7.2 Indices associated to a group and multiplicity results 131
7.3 The Z2 index of Krasnoselski 140
7.4 A relaxed Z2 symmetric mountain pass theorem 141
7.5 Multiple solutions in the presence of symmetry 143
7.6 The mod 2 genus 145
Notes and Comments 146
Chapter 8. The Palais Smale Condition Around
a Dual Set Examples 147
8.1 A positive solution for an elliptic boundary value problem
involving the critical Sobolev exponent 147
8.2 A sign changing solution for an elliptic boundary value
problem involving the critical Sobolev exponent 151
8.3 A second solution for a nonhomogeneous elliptic equation
involving the critical Sobolev exponent 158
Notes and Comments 165
Chapter 9. Morse Indices of Min Max Critical Points
The Non Degenerate Case 166
9.1 Homotopic, cohomotopic and homological families 166
9.2 The Morse Lemma 169
9.3 The transformation of Lazer Solimini 170
9.4 Morse indices in the saddle point theorem 176
9.5 An asymptotically linear non resonant boundary
value problem 176
9.6 An asymptotically linear resonant problem of
Landesman Laser type 178
9.7 An asymptotically linear strongly resonant
boundary value problem 181
Notes and Comments 182
Chapter 10. Morse Indices of Min Max Critical Points
The Degenerate Case 183
10.1 Multiplicity results for critical points with a given
Morse index 183
x Contents
10.2 Restrictions of a homotopy stable class to a neighborhood 187
10.3 The Marino Prodi perturbation method 189
10.4 The reduction to the non degenerate case 193
10.5 Application to some classical variational settings 199
Notes and Comments 203
Chapter 11. Morse type Information on Palais Smale
Sequences 204
11.1 Palais Smale sequences with second order conditions
the homotopic case 205
11.2 Multiple solutions for the Hartree Fock equations 215
11.3 Palais Smale sequences with second order conditions
the cohomotopic case 219
Notes and Comments 223
Appendices by David Robinson
A Relevant function spaces and inequalities 224
B Variational formulations of some
boundary value problems 233
C The blowing up of singularities 236
D Elements of degree theory 238
E Basic properties of martingales 243
References 246
Index 254
|
| any_adam_object | 1 |
| author | Ghoussoub, Nassif 1953- |
| author_GND | (DE-588)137025246 |
| author_facet | Ghoussoub, Nassif 1953- |
| author_role | aut |
| author_sort | Ghoussoub, Nassif 1953- |
| author_variant | n g ng |
| building | Verbundindex |
| bvnumber | BV008243112 |
| classification_rvk | SK 350 SK 600 SK 660 |
| classification_tum | MAT 490f MAT 576f MAT 418f |
| ctrlnum | (OCoLC)246327701 (DE-599)BVBBV008243112 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01969nam a2200481 cb4500</leader><controlfield tag="001">BV008243112</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19940413 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">930929s1993 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521440254</subfield><subfield code="9">0-521-44025-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246327701</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV008243112</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 350</subfield><subfield code="0">(DE-625)143233:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 660</subfield><subfield code="0">(DE-625)143251:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 490f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 576f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 418f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ghoussoub, Nassif</subfield><subfield code="d">1953-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)137025246</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Duality and perturbation methods in critical point theory</subfield><subfield code="c">Nassif Ghoussoub</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge u.a.</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 258 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cambridge tracts in mathematics</subfield><subfield code="v">107</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Störungstheorie</subfield><subfield code="0">(DE-588)4128420-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kritischer Punkt</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4207169-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dualitätstheorie</subfield><subfield code="0">(DE-588)4150801-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kritischer Punkt</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4207169-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Dualitätstheorie</subfield><subfield code="0">(DE-588)4150801-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Kritischer Punkt</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4207169-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Störungstheorie</subfield><subfield code="0">(DE-588)4128420-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge tracts in mathematics</subfield><subfield code="v">107</subfield><subfield code="w">(DE-604)BV000000001</subfield><subfield code="9">107</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005442309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-005442309</subfield></datafield></record></collection> |
| id | DE-604.BV008243112 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:16:58Z |
| institution | BVB |
| isbn | 0521440254 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005442309 |
| oclc_num | 246327701 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-739 DE-20 DE-703 DE-19 DE-BY-UBM DE-634 DE-11 DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-739 DE-20 DE-703 DE-19 DE-BY-UBM DE-634 DE-11 DE-188 |
| physical | XVIII, 258 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Ghoussoub, Nassif 1953- Verfasser (DE-588)137025246 aut Duality and perturbation methods in critical point theory Nassif Ghoussoub 1. publ. Cambridge u.a. Cambridge Univ. Press 1993 XVIII, 258 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 107 Störungstheorie (DE-588)4128420-3 gnd rswk-swf Kritischer Punkt Mathematik (DE-588)4207169-0 gnd rswk-swf Dualitätstheorie (DE-588)4150801-4 gnd rswk-swf Kritischer Punkt Mathematik (DE-588)4207169-0 s Dualitätstheorie (DE-588)4150801-4 s DE-604 Störungstheorie (DE-588)4128420-3 s Cambridge tracts in mathematics 107 (DE-604)BV000000001 107 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005442309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ghoussoub, Nassif 1953- Duality and perturbation methods in critical point theory Cambridge tracts in mathematics Störungstheorie (DE-588)4128420-3 gnd Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Dualitätstheorie (DE-588)4150801-4 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4207169-0 (DE-588)4150801-4 |
| title | Duality and perturbation methods in critical point theory |
| title_auth | Duality and perturbation methods in critical point theory |
| title_exact_search | Duality and perturbation methods in critical point theory |
| title_full | Duality and perturbation methods in critical point theory Nassif Ghoussoub |
| title_fullStr | Duality and perturbation methods in critical point theory Nassif Ghoussoub |
| title_full_unstemmed | Duality and perturbation methods in critical point theory Nassif Ghoussoub |
| title_short | Duality and perturbation methods in critical point theory |
| title_sort | duality and perturbation methods in critical point theory |
| topic | Störungstheorie (DE-588)4128420-3 gnd Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Dualitätstheorie (DE-588)4150801-4 gnd |
| topic_facet | Störungstheorie Kritischer Punkt Mathematik Dualitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005442309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT ghoussoubnassif dualityandperturbationmethodsincriticalpointtheory |