Author | Chang, Kung-ching. author |
---|---|
Title | Infinite Dimensional Morse Theory and Multiple Solution Problems [electronic resource] / by Kung-ching Chang |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0385-8 |
Descript | X, 313 p. online resource |
I: Infinite Dimensional Morse Theory -- 1. A Review of Algebraic Topology -- 2. A Review of the Banach-Finsler Manifold -- 3. Pseudo Gradient Vector Field and the Deformation Theorems -- 4. Critical Groups and Morse Type Numbers -- 5. Gromoll-Meyer Theory -- 6. Extensions of Morse Theory -- 7. Equivariant Morse Theory -- II: Critical Point Theory -- 1. Topological Link -- 2. Morse Indices of Minimax Critical Points -- 3. Connections with Other Theories -- 4. Invariant Functional -- 5. Some Abstract Critical Point Theorems -- 6. Perturbation Theory -- III: Applications to Semilinear Elliptic Boundary Value Problems -- 1. Preliminaries -- 2. Superlinear Problems -- 3. Asymptotically Linear Problems -- 4. Bounded Nonlinearities -- IV: Multiple Periodic Solutions of Hamiltonian Systems -- 1. Asymptotically Linear Systems -- 2. Reductions and Periodic Nonlinearities -- 3. Singular Potentials -- 4. The Multiple Pendulum Equation -- 5. Some Results on Arnold Conjectures -- V: Applications to Harmonic Maps and Minimal Surfaces -- 1. Harmonic Maps and the Heat Flow -- 2. The Morse Inequalities -- 3. Morse Decomposition -- 4. The Existence and Multiplicity for Harmonic Maps -- 5. The Plateau Problem for Minimal Surfaces -- Appendix: Wittenโs Proof of the Morse Inequalities -- 1. A Review of Hodge Theory -- 2. The Witten Complex -- 3. Weak Morse Inequalities -- 4. Morse Inequalities -- References -- Index of Notation