Author | Schechter, Martin. author |
---|---|
Title | Linking Methods in Critical Point Theory [electronic resource] / by Martin Schechter |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1999 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1596-7 |
Descript | XVII, 294 p. online resource |
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?รญk Spectrum -- 7.1 Introduction -- 7.2 Jumping Nonlinearities -- 7.3 Quantities Related to the Fu?รญ k Spectrum -- 7.4 Applications -- 8 Resonance -- 8.1 Introduction -- 8.2 More on Double Resonance -- 8.3 Resonance Involving Many Eigenvalues -- 8.4 LandesmanโLazer 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