Linking Methods in Critical Point Theory - Martin Schechter

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Sommaire:
1 Critical Point Theory.- 1.1 Introduction.- 1.2 Other Geometries.- 1.3 Semilinear Boundary Value Problems.- 1.4 The Critical Point Alternative.- 1.5 The Mountain Cliff Theorem.- 1.6 Estimates on Eigenspaces.- 1.7 Asymptotic Limits.- 1.8 Types of Resonance.- 1.9 Multiple Solutions.- 1.10 Eigenvalues.- 2 Linking.- 2.1 The Basic Concept.- 2.2 The Flow.- 2.3 Weaker Conditions.- 2.4 Another Form.- 2.5 Some Consequences.- 2.6 Examples of Linking.- 2.7 Critical Sequences.- 2.8 The Compact Case.- 2.9 A Sandwich Theorem.- 2.10 Appendix I: Pseudo-Gradients.- 2.11 Appendix II: Differential Equations.- 3 Semilinear Boundary Value Problems.- 3.1 Introduction.- 3.2 Mountain Pass Geometry.- 3.3 Finding a Critical Sequence.- 3.4 Obtaining a Solution.- 3.5 Solving the Problem.- 3.6 Resonance.- 3.7 Appendix I: The Sobolev Inequality.- 4 Alternative Methods 73.- 4.1 Introduction.- 4.2 The Saddle Point Alternative.- 4.3 An Alternate Form.- 4.4 Some Corollaries.- 4.5 An Application.- 4.6 Superlinear Problems.- 4.7 Some Modifications.- 5 Bounded Saddle Point Methods.- 5.1 Introduction.- 5.2 A Bounded Mountain Pass Lemma.- 5.3 The Mountain Pass Alternative.- 5.4 A Compactness Condition.- 5.5 Dual Situations.- 5.6 Combined Results.- 5.7 Nonlinear Eigenvalues.- 5.8 Double Resonance.- 5.9 Appendix I: Generalized Pseudo-Gradients.- 6 Estimates on Subspaces.- 6.1 Introduction.- 6.2 Some Important Quantities.- 6.3 The Estimates.- 6.4 Nontrivial Solutions.- 6.5 A Variation.- 7 The Fu??k Spectrum.- 7.1 Introduction.- 7.2 Jumping Nonlinearities.- 7.3 Quantities Related to the Fu?? k Spectrum.- 7.4 Applications.- 8 Resonance.- 8.1 Introduction.- 8.2 More on Double Resonance.- 8.3 Resonance Involving Many Eigenvalues.- 8.4 Landesman?Lazer Resonance.- 8.5 Equal Limits at Infinity.- 8.6 Nonvanishing Solutions.- 8.7 Unequal Limits at Infinity.- 9 Boundary Conditions.- 9.1 Introduction.- 9.2 Bounded Linking.- 9.3 Reverse Boundary Conditions.- 9.4 An Application.- 9.5 Sufficient Conditions.- 10 Multiple Solutions.- 10.1 Introduction.- 10.2 The Abstract Theory.- 10.3 Some Applications.- 10.4 Additional Solutions.- 11 Nonlinear Eigenvalues.- 11.1 Introduction.- 11.2 The Hampwile Theorem.- 11.3 Applications.- 12 Strong Resonance.- 12.1 Introduction.- 12.2 Simple Solutions.- 12.3 A Different Approach.- 12.4 Resonance at the First Eigenvalue.- 12.5 Additional Solutions.- 13 Notes, Remarks and References.