Nonlinear analysis and semilinear elliptic problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
104 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Beschreibung für Leser Publisher description Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 309-314) and index |
| Beschreibung: | xi, 316 S. graph. Darst. 24 cm |
| ISBN: | 0521863201 9780521863209 |
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Datensatz im Suchindex
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| adam_text | NONLINEAR ANALYSIS AND SEMILINEAR ELLIPTIC PROBLEMS ANTONIO AMBROSETTI
ANDREA MALCHIODI CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE IX 1
PRELIMINARIES 1 1.1 DIFFERENTIAL CALCULUS 1 1.2 FUNCTION SPACES 4 1.3
NEMITSKI OPERATORS 5 1.4 ELLIPTIC EQUATIONS 7 PARTI TOPOLOGICAL METHODS
13 2 A PRIMER ON BIFURCATION THEORY 15 2.1 BIFURCATION: DEFINITION AND
NECESSARY CONDITIONS 15 2.2 THE LYAPUNOV-SCHMIDT REDUCTION 18 2.3
BIFURCATION FROM THE SIMPLE EIGENVALUE 19 3 TOPOLOGICAL DEGREE, I 26 3.1
BROUWER DEGREE AND ITS PROPERTIES 26 3.2 APPLICATION: THE BROUWER FIXED
POINT THEOREM 30 3.3 AN ANALYTIC DEFINITION OF THE DEGREE 31 3.4 THE
LERAY-SCHAUDER DEGREE 38 3.5 THE SCHAUDER FIXED POINT THEOREM 43 3.6
SOME APPLICATIONS OF THE LERAY-SCHAUDER DEGREE TO ELLIPTIC EQUATIONS 44
3.7 THE KRASNOSELSKI BIFURCATION THEOREM 52 3.8 EXERCISES 54 4
TOPOLOGICAL DEGREE, II: GLOBAL PROPERTIES 55 4.1 IMPROVING THE HOMOTOPY
INVARIANCE 55 4.2 AN APPLICATION TO A BOUNDARY VALUE PROBLEM WITH SUB-
AND SUPER-SOLUTIONS 57 VI CONTENTS 4.3 THE RABINOWITZ GLOBAL BIFURCATION
THEOREM 60 4.4 BIFURCATION FROM INFINITY AND POSITIVE SOLUTIONS OF
ASYMPTOTICALLY LINEAR ELLIPTIC PROBLEMS 65 4.5 EXERCISES 73 PART II
VARIATIONAL METHODS, I 75 5 CRITICAL POINTS: EXTREMA 77 5.1 FUNCTIONALS
AND CRITICAL POINTS 77 5.2 GRADIENTS 78 5.3 EXISTENCE OF EXTREMA 80 5.4
SOME APPLICATIONS 82 5.5 LINEAR EIGENVALUES 86 5.6 EXERCISES 88 6
CONSTRAINED CRITICAL POINTS 89 6.1 DIFFERENTIABLE MANIFOLDS, AN OUTLINE
89 6.2 CONSTRAINED CRITICAL POINTS 93 6.3 MANIFOLDS OF CODIMENSION ONE
95 6.4 NATURAL CONSTRAINTS 97 7 DEFORMATIONS AND THE PALAIS-SMALE
CONDITION 100 7.1 DEFORMATIONS OF SUBLEVELS 100 7.2 THE STEEPEST DESCENT
FLOW 101 7.3 DEFORMATIONS AND COMPACTNESS 105 7.4 THE PALAIS-SMALE
CONDITION 107 7.5 EXISTENCE OF CONSTRAINED MINIMA 109 7.6 AN APPLICATION
TO A SUPERLINEAR DIRICHLET PROBLEM 109 7.7 EXERCISES 114 8 SADDLE
POINTS AND MIN-MAX METHODS 116 8.1 THE MOUNTAIN PASS THEOREM 117 8.2
APPLICATIONS 123 8.3 LINKING THEOREMS 129 8.4 THE POHOZAEV IDENTITY 135
8.5 EXERCISES 138 PART III VARIATIONAL METHODS, II 141 9
LUSTERNIK-SCHNIRELMAN THEORY 143 9.1 THE LUSTERNIK-SCHNIRELMAN CATEGORY
143 CONTENTS VII 9.2 LUSTERNIK-SCHNIRELMAN THEOREMS 147 9.3 EXERCISES
155 10 CRITICAL POINTS OF EVEN FUNCTIONALS ON SYMMETRIC MANIFOLDS 1 57
10.1 THE KRASNOSELSKI GENUS 157 10.2 EXISTENCE OF CRITICAL POINTS 160
10.3 MULTIPLE CRITICAL POINTS OF EVEN UNBOUNDED FUNCTIONALS 164 10.4
APPLICATIONS TO DIRICHLET BOUNDARY VALUE PROBLEMS 170 10.5 EXERCISES 176
11 FURTHER RESULTS ON ELLIPTIC DIRICHLET PROBLEMS 177 11.1 RADIAL
SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATION ON W 177 11.2 BOUNDARY VALUE
PROBLEMS WITH CRITICAL EXPONENT 180 11.3 DISCONTINUOUS NONLINEARITIES
188 11.4 PROBLEMS WITH CONCAVE-CONVEX NONLINEARITIES 198 11.5 EXERCISES
203 12 MORSE THEORY 204 12.1 A SHORT REVIEW OF BASIC FACTS IN ALGEBRAIC
TOPOLOGY. 204 12.2 THE MORSE INEQUALITIES 212 12.3 AN APPLICATION:
BIFURCATION FOR VARIATIONAL OPERATORS 224 12.4 MORSE INDEX OF MOUNTAIN
PASS CRITICAL POINTS 229 12.5 EXERCISES 235 PART IV APPENDICES 233
APPENDIX 1 QUALITATIVE RESULTS 241 APPENDIX 2 THE CONCENTRATION
COMPACTNESS PRINCIPLE 252 APPENDIX 3 BIFURCATION FOR PROBLEMS ON R ,
262 APPENDIX 4 VORTE X RINGS IN AN IDEAL FLUID 274 APPENDIX 5
PERTURBATION METHODS 286 APPENDIX 6 SOME PROBLEMS ARISING IN
DIFFERENTIAL GEOMETRY 302 REFERENCES 309 INDEX 315
|
| adam_txt |
NONLINEAR ANALYSIS AND SEMILINEAR ELLIPTIC PROBLEMS ANTONIO AMBROSETTI
ANDREA MALCHIODI CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE IX 1
PRELIMINARIES 1 1.1 DIFFERENTIAL CALCULUS 1 1.2 FUNCTION SPACES 4 1.3
NEMITSKI OPERATORS 5 1.4 ELLIPTIC EQUATIONS 7 PARTI TOPOLOGICAL METHODS
13 2 A PRIMER ON BIFURCATION THEORY 15 2.1 BIFURCATION: DEFINITION AND
NECESSARY CONDITIONS 15 2.2 THE LYAPUNOV-SCHMIDT REDUCTION 18 2.3
BIFURCATION FROM THE SIMPLE EIGENVALUE 19 3 TOPOLOGICAL DEGREE, I 26 3.1
BROUWER DEGREE AND ITS PROPERTIES 26 3.2 APPLICATION: THE BROUWER FIXED
POINT THEOREM 30 3.3 AN ANALYTIC DEFINITION OF THE DEGREE 31 3.4 THE
LERAY-SCHAUDER DEGREE 38 3.5 THE SCHAUDER FIXED POINT THEOREM 43 3.6
SOME APPLICATIONS OF THE LERAY-SCHAUDER DEGREE TO ELLIPTIC EQUATIONS 44
3.7 THE KRASNOSELSKI BIFURCATION THEOREM 52 3.8 EXERCISES 54 4
TOPOLOGICAL DEGREE, II: GLOBAL PROPERTIES 55 4.1 IMPROVING THE HOMOTOPY
INVARIANCE 55 4.2 AN APPLICATION TO A BOUNDARY VALUE PROBLEM WITH SUB-
AND SUPER-SOLUTIONS 57 VI CONTENTS 4.3 THE RABINOWITZ GLOBAL BIFURCATION
THEOREM 60 4.4 BIFURCATION FROM INFINITY AND POSITIVE SOLUTIONS OF
ASYMPTOTICALLY LINEAR ELLIPTIC PROBLEMS 65 4.5 EXERCISES 73 PART II
VARIATIONAL METHODS, I 75 5 CRITICAL POINTS: EXTREMA 77 5.1 FUNCTIONALS
AND CRITICAL POINTS 77 5.2 GRADIENTS 78 5.3 EXISTENCE OF EXTREMA 80 5.4
SOME APPLICATIONS 82 5.5 LINEAR EIGENVALUES 86 5.6 EXERCISES 88 6
CONSTRAINED CRITICAL POINTS 89 6.1 DIFFERENTIABLE MANIFOLDS, AN OUTLINE
89 6.2 CONSTRAINED CRITICAL POINTS 93 6.3 MANIFOLDS OF CODIMENSION ONE
95 6.4 NATURAL CONSTRAINTS 97 7 DEFORMATIONS AND THE PALAIS-SMALE
CONDITION 100 7.1 DEFORMATIONS OF SUBLEVELS 100 7.2 THE STEEPEST DESCENT
FLOW 101 7.3 DEFORMATIONS AND COMPACTNESS 105 7.4 THE PALAIS-SMALE
CONDITION 107 7.5 EXISTENCE OF CONSTRAINED MINIMA 109 7.6 AN APPLICATION
TO A SUPERLINEAR DIRICHLET PROBLEM 109 7.7 EXERCISES ' 114 8 SADDLE
POINTS AND MIN-MAX METHODS 116 8.1 THE MOUNTAIN PASS THEOREM 117 8.2
APPLICATIONS 123 8.3 LINKING THEOREMS 129 8.4 THE POHOZAEV IDENTITY 135
8.5 EXERCISES 138 PART III VARIATIONAL METHODS, II 141 9
LUSTERNIK-SCHNIRELMAN THEORY 143 9.1 THE LUSTERNIK-SCHNIRELMAN CATEGORY
143 CONTENTS VII 9.2 LUSTERNIK-SCHNIRELMAN THEOREMS 147 9.3 EXERCISES
155 10 CRITICAL POINTS OF EVEN FUNCTIONALS ON SYMMETRIC MANIFOLDS 1 57
10.1 THE KRASNOSELSKI GENUS 157 10.2 EXISTENCE OF CRITICAL POINTS 160
10.3 MULTIPLE CRITICAL POINTS OF EVEN UNBOUNDED FUNCTIONALS 164 10.4
APPLICATIONS TO DIRICHLET BOUNDARY VALUE PROBLEMS 170 10.5 EXERCISES 176
11 FURTHER RESULTS ON ELLIPTIC DIRICHLET PROBLEMS 177 11.1 RADIAL
SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATION ON W 177 11.2 BOUNDARY VALUE
PROBLEMS WITH CRITICAL EXPONENT 180 11.3 DISCONTINUOUS NONLINEARITIES
188 11.4 PROBLEMS WITH CONCAVE-CONVEX NONLINEARITIES 198 11.5 EXERCISES
203 12 MORSE THEORY 204 12.1 A SHORT REVIEW OF BASIC FACTS IN ALGEBRAIC
TOPOLOGY. 204 12.2 THE MORSE INEQUALITIES 212 12.3 AN APPLICATION:
BIFURCATION FOR VARIATIONAL OPERATORS 224 12.4 MORSE INDEX OF MOUNTAIN
PASS CRITICAL POINTS 229 12.5 EXERCISES 235 PART IV APPENDICES 233
APPENDIX 1 QUALITATIVE RESULTS 241 APPENDIX 2 THE CONCENTRATION
COMPACTNESS PRINCIPLE 252 APPENDIX 3 BIFURCATION FOR PROBLEMS ON R" ,
262 APPENDIX 4 VORTE X RINGS IN AN IDEAL FLUID 274 APPENDIX 5
PERTURBATION METHODS 286 APPENDIX 6 SOME PROBLEMS ARISING IN
DIFFERENTIAL GEOMETRY 302 REFERENCES 309 INDEX 315 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T18:48:51Z |
| indexdate | 2024-07-09T21:07:30Z |
| institution | BVB |
| isbn | 0521863201 9780521863209 |
| language | English |
| lccn | 2007295323 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016080613 |
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| physical | xi, 316 S. graph. Darst. 24 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Ambrosetti, Antonio 1944-2020 Verfasser (DE-588)111667070 aut Nonlinear analysis and semilinear elliptic problems Antonio Ambrosetti, Andrea Malchiodi 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 xi, 316 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 104 Includes bibliographical references (p. 309-314) and index Nonlinear theories Differential equations, Elliptic Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 s DE-604 Semilineare elliptische Differentialgleichung (DE-588)4225683-5 s Malchiodi, Andrea Sonstige (DE-588)130563021 oth Cambridge studies in advanced mathematics 104 (DE-604)BV000003678 104 http://catdir.loc.gov/catdir/enhancements/fy0713/2007295323-t.html Inhaltsverzeichnis http://catdir.loc.gov/catdir/enhancements/fy0713/2007295323-d.html Beschreibung für Leser http://www.loc.gov/catdir/enhancements/fy0713/2007295323-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0713/2007295323-t.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016080613&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ambrosetti, Antonio 1944-2020 Nonlinear analysis and semilinear elliptic problems Cambridge studies in advanced mathematics Nonlinear theories Differential equations, Elliptic Nichtlineare Analysis (DE-588)4177490-5 gnd Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd |
| subject_GND | (DE-588)4177490-5 (DE-588)4225683-5 |
| title | Nonlinear analysis and semilinear elliptic problems |
| title_auth | Nonlinear analysis and semilinear elliptic problems |
| title_exact_search | Nonlinear analysis and semilinear elliptic problems |
| title_exact_search_txtP | Nonlinear analysis and semilinear elliptic problems |
| title_full | Nonlinear analysis and semilinear elliptic problems Antonio Ambrosetti, Andrea Malchiodi |
| title_fullStr | Nonlinear analysis and semilinear elliptic problems Antonio Ambrosetti, Andrea Malchiodi |
| title_full_unstemmed | Nonlinear analysis and semilinear elliptic problems Antonio Ambrosetti, Andrea Malchiodi |
| title_short | Nonlinear analysis and semilinear elliptic problems |
| title_sort | nonlinear analysis and semilinear elliptic problems |
| topic | Nonlinear theories Differential equations, Elliptic Nichtlineare Analysis (DE-588)4177490-5 gnd Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd |
| topic_facet | Nonlinear theories Differential equations, Elliptic Nichtlineare Analysis Semilineare elliptische Differentialgleichung |
| url | http://catdir.loc.gov/catdir/enhancements/fy0713/2007295323-t.html http://catdir.loc.gov/catdir/enhancements/fy0713/2007295323-d.html http://www.loc.gov/catdir/enhancements/fy0713/2007295323-d.html http://www.loc.gov/catdir/enhancements/fy0713/2007295323-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016080613&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT ambrosettiantonio nonlinearanalysisandsemilinearellipticproblems AT malchiodiandrea nonlinearanalysisandsemilinearellipticproblems |
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