Handbook of applied analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Springer
2009
|
| Schriftenreihe: | Advances in mechanics and mathematics
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 793 S. |
| ISBN: | 9780387789064 9780387789071 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804137795168501760 |
|---|---|
| adam_text | Titel: Handbook of Applied Analysis
Autor: Papageorgiou, Nikolaos Socrates
Jahr: 2009
Contents
Series Preface ................................................. ix
Preface........................................................ xi
1 Smooth and Nonsmooth Calculus.......................... 1
1.1 Gateaux and Frechet Derivatives.......................... 2
1.2 Convex Functions ....................................... 12
1.3 Locally Lipschitz Functions............................... 27
1.4 Variational Geometry.................................... 35
1.5 F-Convergence.......................................... 45
1.6 Remarks ............................................... 60
2 Extremal Problems and Optimal Control.................. 63
2.1 Lower Semicontinuity.................................... 64
2.2 Constrained Minimization Problems....................... 72
2.3 Saddle Points and Duality................................ 79
2.4 Variational Principles.................................... 89
2.5 Calculus of Variations.................................... 98
2.6 Optimal Control ........................................Ill
2.7 Remarks ...............................................144
3 Nonlinear Operators and Fixed Points.....................147
3.1 Compact and Fredholm Operators.........................148
3.2 Monotone and Accretive Operators........................162
3.3 Degree Theory..........................................196
3.4 Metric Fixed Points......................................224
3.5 Topological Fixed Points.................................237
3.6 Order and Fixed Points ..................................245
3.7 Remarks ...............................................263
xvi Contents
4 Critical Point Theory and Variational Methods............267
4.1 Critical Point Theory....................................268
4.2 Ljusternik Sclmirelinann Theory..........................289
4.3 Spectrum of the Laplacian and of the p-Laplacian...........297
4.4 Abstract Eigenvalue Problems.............................334
4.5 Bifurcation Theory......................................340
4.0 Remarks ...............................................349
5 Boundary Value Problems-Hamiltonian Systems ..........351
5.1 Variational Method......................................352
5.2 Method of Upper-Lower Solutions.........................380
5.3 Degree-Theoretic Methods................................404
5.4 Nonlinear Eigenvalue Problems............................421
5.5 Maximum and Comparison Principles......................432
5.6 Periodic Solutions for Hamiltoniaa Systems.................440
5.7 Remarks ...............................................450
6 Multivalued Analysis......................................455
6.1 Continuity of Multifunctions..............................456
6.2 Measurability of Multifunctions...........................470
6.3 Continuous and Measurable Selectors......................475
6.4 Decomposable Sets and Set-Valued Integration..............487
6.5 Fixed Points and Caratheodory Multifunctions..............504
0.0 Convergence of Sets......................................514
6.7 Remarks ...............................................524
7 Economic Equilibrium and Optimal Economic Planning . . . 529
7.1 Perfectly Competitive Economies: Core and Walras Equilibria 530
7.2 Infinite Horizon Multisector Growth Models ................542
7.3 Turnpike Theorems......................................558
7.4 Stochastic Growth Models................................507
7.5 Continuous-Time Growth Models..........................589
7.6 Expected Utility Hypothesis..............................599
7.7 Remarks ...............................................606
8 Game Theory..............................................609
5.1 Nonrooperative Games Nash Equilibrium ..................010
8.2 Cooperative Games......................................617
5.3 Cournot Nash Equilibria for Random Games ...............624
8.4 Bayesian Games.........................................628
N.5 Stochastic Games........................................032
8.6 Approximate Equilibria..................................( 44
8.7 Remarks ...............................................049
Contents xvii
9 Uncertainty, Information, Decision Making................651
9.1 Mathematical Space of Information........................652
9.2 The ex-Post View .......................................662
9.3 The ex-ante View .......................................668
9.4 Convergence of r-Fields and Prediction Sequences...........673
9.T Games with Incomplete Information.......................680
9.6 Markov Decision Chains with Unbounded Costs.............684
9.7 Remarks ...............................................689
10 Evolution Equations.......................................691
10.1 Lebesgue-Bochner Spaces ................................692
10.2 Seinilinear Evolution Equations ...........................701
10.3 Nonlinear Evolution Equations............................718
10.4 Second-Order Nonlinear Evolution Equations ...............740
10.5 Remarks ...............................................750
References.....................................................753
List of Symbols................................................781
Index..........................................................783
|
| adam_txt |
Titel: Handbook of Applied Analysis
Autor: Papageorgiou, Nikolaos Socrates
Jahr: 2009
Contents
Series Preface . ix
Preface. xi
1 Smooth and Nonsmooth Calculus. 1
1.1 Gateaux and Frechet Derivatives. 2
1.2 Convex Functions . 12
1.3 Locally Lipschitz Functions. 27
1.4 Variational Geometry. 35
1.5 F-Convergence. 45
1.6 Remarks . 60
2 Extremal Problems and Optimal Control. 63
2.1 Lower Semicontinuity. 64
2.2 Constrained Minimization Problems. 72
2.3 Saddle Points and Duality. 79
2.4 Variational Principles. 89
2.5 Calculus of Variations. 98
2.6 Optimal Control .Ill
2.7 Remarks .144
3 Nonlinear Operators and Fixed Points.147
3.1 Compact and Fredholm Operators.148
3.2 Monotone and Accretive Operators.162
3.3 Degree Theory.196
3.4 Metric Fixed Points.224
3.5 Topological Fixed Points.237
3.6 Order and Fixed Points .245
3.7 Remarks .263
xvi Contents
4 Critical Point Theory and Variational Methods.267
4.1 Critical Point Theory.268
4.2 Ljusternik Sclmirelinann Theory.289
4.3 Spectrum of the Laplacian and of the p-Laplacian.297
4.4 Abstract Eigenvalue Problems.334
4.5 Bifurcation Theory.340
4.0 Remarks .349
5 Boundary Value Problems-Hamiltonian Systems .351
5.1 Variational Method.352
5.2 Method of Upper-Lower Solutions.380
5.3 Degree-Theoretic Methods.404
5.4 Nonlinear Eigenvalue Problems.421
5.5 Maximum and Comparison Principles.432
5.6 Periodic Solutions for Hamiltoniaa Systems.440
5.7 Remarks .450
6 Multivalued Analysis.455
6.1 Continuity of Multifunctions.456
6.2 Measurability of Multifunctions.470
6.3 Continuous and Measurable Selectors.475
6.4 Decomposable Sets and Set-Valued Integration.487
6.5 Fixed Points and Caratheodory Multifunctions.504
0.0 Convergence of Sets.514
6.7 Remarks .524
7 Economic Equilibrium and Optimal Economic Planning . . . 529
7.1 Perfectly Competitive Economies: Core and Walras Equilibria 530
7.2 Infinite Horizon Multisector Growth Models .542
7.3 Turnpike Theorems.558
7.4 Stochastic Growth Models.507
7.5 Continuous-Time Growth Models.589
7.6 Expected Utility Hypothesis.599
7.7 Remarks .606
8 Game Theory.609
5.1 Nonrooperative Games Nash Equilibrium .010
8.2 Cooperative Games.617
5.3 Cournot Nash Equilibria for Random Games .624
8.4 Bayesian Games.628
N.5 Stochastic Games.032
8.6 Approximate Equilibria.( 44
8.7 Remarks .049
Contents xvii
9 Uncertainty, Information, Decision Making.651
9.1 Mathematical Space of Information.652
9.2 The ex-Post View .662
9.3 The ex-ante View .668
9.4 Convergence of r-Fields and Prediction Sequences.673
9.T Games with Incomplete Information.680
9.6 Markov Decision Chains with Unbounded Costs.684
9.7 Remarks .689
10 Evolution Equations.691
10.1 Lebesgue-Bochner Spaces .692
10.2 Seinilinear Evolution Equations .701
10.3 Nonlinear Evolution Equations.718
10.4 Second-Order Nonlinear Evolution Equations .740
10.5 Remarks .750
References.753
List of Symbols.781
Index.783 |
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| index_date | 2024-07-02T21:26:37Z |
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| isbn | 9780387789064 9780387789071 |
| language | English |
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| spelling | Papageōrgiu, Nikolaos 1958- Verfasser (DE-588)137051085 aut Handbook of applied analysis by Nikolaos S. Papageorgiou ; Sophia Th. Kyritsi-Yiallourou Dordrecht [u.a.] Springer 2009 XVII, 793 S. txt rdacontent n rdamedia nc rdacarrier Advances in mechanics and mathematics 19 Mathematical analysis Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 s DE-604 Kyritsi-Yiallourou, Sophia Th. 20./21. Jh. Verfasser (DE-588)138791090 aut Advances in mechanics and mathematics 19 (DE-604)BV017903734 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016591286&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Papageōrgiu, Nikolaos 1958- Kyritsi-Yiallourou, Sophia Th. 20./21. Jh Handbook of applied analysis Advances in mechanics and mathematics Mathematical analysis Nichtlineare Analysis (DE-588)4177490-5 gnd |
| subject_GND | (DE-588)4177490-5 |
| title | Handbook of applied analysis |
| title_auth | Handbook of applied analysis |
| title_exact_search | Handbook of applied analysis |
| title_exact_search_txtP | Handbook of applied analysis |
| title_full | Handbook of applied analysis by Nikolaos S. Papageorgiou ; Sophia Th. Kyritsi-Yiallourou |
| title_fullStr | Handbook of applied analysis by Nikolaos S. Papageorgiou ; Sophia Th. Kyritsi-Yiallourou |
| title_full_unstemmed | Handbook of applied analysis by Nikolaos S. Papageorgiou ; Sophia Th. Kyritsi-Yiallourou |
| title_short | Handbook of applied analysis |
| title_sort | handbook of applied analysis |
| topic | Mathematical analysis Nichtlineare Analysis (DE-588)4177490-5 gnd |
| topic_facet | Mathematical analysis Nichtlineare Analysis |
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