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| Preface | |
| Introduction | |
| Infinite Dimensional Morse Theory | |
| A Review of Algebraic Topology | p. 1 |
| A Review of the Banach-Finsler Manifold | p. 14 |
| Pseudo Gradient Vector Field and the Deformation Theorems | p. 19 |
| Critical Groups and Morse Type Numbers | p. 32 |
| Gromoll-Meyer Theory | p. 43 |
| Extensions of Morse Theory | p. 54 |
| Morse Theory Under General Boundary Conditions | p. 55 |
| Morse Theory on a Locally Convex Closed Set | p. 60 |
| Equivariant Morse Theory | p. 65 |
| Preliminaries | p. 66 |
| Equivariant Deformation | p. 67 |
| The Splitting Theorem and the Handle Body Theorem for Critical Manifolds | p. 69 |
| G-Cohomology and G-Critical Groups | p. 74 |
| Critical Point Theory | |
| Topological Link | p. 83 |
| Morse Indices of Minimax Critical Points | p. 92 |
| Link | p. 92 |
| Genus and Cogenus | p. 96 |
| Connections with Other Theories | p. 99 |
| Degree theory | p. 99 |
| Ljusternik-Schnirelman Theory | p. 105 |
| Relative Category | p. 109 |
| Invariant Functionals | p. 111 |
| Some Abstract Critical Point Theorems | p. 121 |
| Perturbation Theory | p. 131 |
| Perturbation on Critical Manifolds | p. 131 |
| Uhlenbeck's Perturbation Method | p. 136 |
| Applications to Semilinear Elliptic Boundary Value Problems | |
| Preliminaries | p. 140 |
| Superlinear Problems | p. 144 |
| Asymptotically Linear Problems | p. 153 |
| Nonresonance and Resonance with the Landesman-Lazer Condition | p. 153 |
| Strong Resonance | p. 156 |
| A Bifurcation Problem | p. 161 |
| Jumping Nonlinearities | p. 164 |
| Other Examples | p. 169 |
| Bounded Nonlinearities | p. 172 |
| Functionals Bounded From Below | p. 172 |
| Oscillating Nonlinearity | p. 173 |
| Even Functionals | p. 176 |
| Variational Inequalities | p. 177 |
| Multiple Periodic Solutions of Hamiltonian Systems | |
| Asymptotically Linear Systems | p. 182 |
| Reductions and Periodic Nonlinearities | p. 188 |
| Saddle Point Reduction | p. 188 |
| A Multiple Solution Theorem | p. 195 |
| Periodic Nonlinearity | p. 198 |
| Singular Potentials | p. 203 |
| The Multiple Pendulum Equation | p. 209 |
| Some Results on Arnold Conjectures | p. 215 |
| Conjectures | p. 215 |
| The Fixed Point Conjecture on (T[superscript 2n, [omega][subscript 0]) | p. 218 |
| Lagrange Intersections for (CP[superscript n], RP[superscript n]) | p. 220 |
| Applications to Harmonic Maps and Minimal Surfaces | |
| Harmonic Maps and the Heat Flow | p. 229 |
| The Morse Inequalities | p. 246 |
| Morse Decomposition | p. 250 |
| The Existence and Multiplicity for Harmonic Maps | p. 257 |
| The Plateau Problem for Minimal Surfaces | p. 260 |
| Appendix: Witten's Proof of the Morse Inequalities | |
| 1. A Review of Hodge Theory | p. 274 |
| 2. The Witten Complex | p. 282 |
| 3. Weak Morse Inequalities | p. 287 |
| 4. Morse Inequalities | p. 295 |
| References | p. 298 |
| Index of Notation | p. 310 |
| Index | p. 311 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
Infinite Dimensional Morse Theory and Multiple Solution Problems
by Chang, Kung-ChingFormat: Hardcover
Pub. Date: 1993-02-01
Publisher(s): Birkhauser
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