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Linking methods in critical point theory:

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Bibliographic Details
Main Author:	Schechter, Martin 1930- (Author)
Format:	Book
Language:	German
Published:	Boston ; Basel ; Berlin Birkhäuser 1999
Subjects:	Points critiques, Théorie des (Analyse mathématique) Problèmes aux limites Boundary value problems Critical point theory (Mathematical analysis) Kritischer Punkt > Mathematik Randwertproblem
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Bibliogr. S. 269 - 292
Physical Description:	XVI, 294 S.
ISBN:	3764340959 0817640959

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Record in the Search Index

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adam_text	Contents FOREWORD ix PREFACE xi 1 CRITICAL POINT THEORY 1 1.1 Introduction 1 1.2 Other Geometries 5 1.3 Semilinear Boundary Value Problems 7 1.4 The Critical Point Alternative 9 1.5 The Mountain Cliff Theorem 9 1.6 Estimates on Eigenspaces 11 1.7 Asymptotic Limits 13 1.8 Types of Resonance 14 1.9 Multiple Solutions 16 1.10 Eigenvalues 17 2 LINKING 21 2.1 The Basic Concept 21 2.2 The Flow 23 2.3 Weaker Conditions 27 2.4 Another Form 30 2.5 Some Consequences 33 2.6 Examples of Linking 36 2.7 Critical Sequences 42 2.8 The Compact Case 45 2.9 A Sandwich Theorem 48 2.10 Appendix I: Pseudo Gradients 51 2.11 Appendix II: Differential Equations 52 v vi CONTENTS 3 SEMILINEAR BOUNDARY VALUE PROBLEMS 55 3.1 Introduction 55 3.2 Mountain Pass Geometry 58 3.3 Finding a Critical Sequence 62 3.4 Obtaining a Solution 63 3.5 Solving the Problem 66 3.6 Resonance 68 3.7 Appendix I: The Sobolev Inequality 72 4 ALTERNATIVE METHODS 73 4.1 Introduction 73 4.2 The Saddle Point Alternative 74 4.3 An Alternate Form 78 4.4 Some Corollaries 81 4.5 An Application 85 4.6 Superlinear Problems 91 4.7 Some Modifications 95 5 BOUNDED SADDLE POINT METHODS 99 5.1 Introduction 99 5.2 A Bounded Mountain Pass Lemma 100 5.3 The Mountain Pass Alternative 105 5.4 A Compactness Condition 107 5.5 Dual Situations 110 5.6 Combined Results 113 5.7 Nonlinear Eigenvalues 117 5.8 Double Resonance 121 5.9 Appendix I: Generalized Pseudo Gradients 128 6 ESTIMATES ON SUBSPACES 131 6.1 Introduction 131 6.2 Some Important Quantities 132 6.3 The Estimates 137 6.4 Nontrivial Solutions 140 6.5 A Variation 142 7 THE FUCIK SPECTRUM 145 7.1 Introduction 145 7.2 Jumping Nonlinearities 146 7.3 Quantities Related to the Fuci k Spectrum 148 CONTENTS vii 7.4 Applications 163 8 RESONANCE 167 8.1 Introduction 167 8.2 More on Double Resonance 168 8.3 Resonance Involving Many Eigenvalues 171 8.4 Landesman Lazer Resonance 176 8.5 Equal Limits at Infinity 185 8.6 Nonvanishing Solutions 192 8.7 Unequal Limits at Infinity 197 9 BOUNDARY CONDITIONS 205 9.1 Introduction 205 9.2 Bounded Linking 205 9.3 Reverse Boundary Conditions 209 9.4 An Application 212 9.5 Sufficient Conditions 215 10 MULTIPLE SOLUTIONS 219 10.1 Introduction 219 10.2 The Abstract Theory 219 10.3 Some Applications 222 10.4 Additional Solutions 227 11 NONLINEAR EIGENVALUES 229 11.1 Introduction 229 11.2 The Hampwile Theorem 230 11.3 Applications 236 12 STRONG RESONANCE 239 12.1 Introduction 239 12.2 Simple Solutions 240 12.3 A Different Approach 243 12.4 Resonance at the First Eigenvalue 246 12.5 Additional Solutions 251 13 NOTES, REMARKS and REFERENCES 255 BIBLIOGRAPHY 269 INDEX 293
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spellingShingle	Schechter, Martin 1930- Linking methods in critical point theory Points critiques, Théorie des (Analyse mathématique) Problèmes aux limites Boundary value problems Critical point theory (Mathematical analysis) Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Randwertproblem (DE-588)4048395-2 gnd
subject_GND	(DE-588)4207169-0 (DE-588)4048395-2
title	Linking methods in critical point theory
title_auth	Linking methods in critical point theory
title_exact_search	Linking methods in critical point theory
title_full	Linking methods in critical point theory Martin Schechter
title_fullStr	Linking methods in critical point theory Martin Schechter
title_full_unstemmed	Linking methods in critical point theory Martin Schechter
title_short	Linking methods in critical point theory
title_sort	linking methods in critical point theory
topic	Points critiques, Théorie des (Analyse mathématique) Problèmes aux limites Boundary value problems Critical point theory (Mathematical analysis) Kritischer Punkt Mathematik (DE-588)4207169-0 gnd Randwertproblem (DE-588)4048395-2 gnd
topic_facet	Points critiques, Théorie des (Analyse mathématique) Problèmes aux limites Boundary value problems Critical point theory (Mathematical analysis) Kritischer Punkt Mathematik Randwertproblem
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008435687&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT schechtermartin linkingmethodsincriticalpointtheory

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Call Number:	0102 MAT 260f 2001 A 30433 Floor plan
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