Contents
Preface vii
An Overview ix
Chapter 0. Morse Theory and Variational Problems 1
0.1. Compactness Conditions 2
0.2. Deformation Lemmas 2
0.3. Critical Groups 3
0.4. Minimax Principle 7
0.5. Linking 8
0.6. Local Linking 10
0.7. p-Laplacian 11
Chapter 1. Abstract Formulation and Examples 17
1.1. p-Laplacian Problems 20
1.2. Ap-Laplacian Problems 20
1.3. Problems in Weighted Sobolev Spaces 21
1.4. q-Kirchhoff Problems 22
1.5. Dynamic Equations on Time Scales 22
1.6. Other Boundary Conditions 23
1.7. p-Biharmonic Problems 25
1.8. Systems of Equations 25
Chapter 2. Background Material 27
2.1. Homotopy 28
2.2. Direct Limits 29
2.3. Alexander-Spanier Cohomology Theory 30
2.4. Principal Z2-Bundles 34
2.5. Cohomological Index 36
Chapter 3. Critical Point Theory 45
3.1. Compactness Conditions 46
3.2. Deformation Lemmas 47
3.3. Minimax Principle 52
3.4. Critical Groups 53
3.5. Minimizers and Maximizers 55
3.6. Homotopical Linking 56
3.7. Cohomological Linking 58
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