目錄
Preface to New Edition
Preface
Chapter 1. Topological Approach: Finite Dimensions
1.1. A Simple Remark
1.2. Sard's Theorem
1.3. Finite-Dimensional Degree Theory
1.4. Properties of Degree
1.5. Further Properties and Remarks
1.6. Some Applications to Nonlinear Equations
1.7. Borsuk's Theorem
1.8. Mappings in Different Dimensions
Chapter 2. Topological Degree in Banach Space
2.1. Schauder Fixed-Point Theorem
2.2. An Application
2.3. Leray-Schauder Degree
2.4. Some Compact Operators
2.5. Elliptic Partial Differential Equations
2.6. Mildly Nonlinear Perturbations of l.inear Operators
2.7. Calculus in Banach Space
2.8. The Leray-Schauder Degree for Isolated Solutions, the Index
Chapter 3. Bifurcation Theory
3.1. The Morse Lemma
3.2. Application of the Morse Lemma
3.3. Krasnoselski's Theorem
3.4. A Theorem of Rabinowitz
3.5. Extension of Krasnoselski's Theorem
3.6. Stability of Solutions
3.7. The Number of Global Solutions of a Nonlinear Problem
Chapter 4. Further Topological Methods
4.1. Extension of Leray-Schauder Degree
4.2. Applications to Partial Differential Equations
4.3. Framed Cobordism
4.4. Stable Cohomotopy Theorem
4.5. Cohomotopy Groups
4.6. Stable Cohomotopy Theory
4.7. Application to Existence of Global Solutions
Chapter 5. Monotone Operators and the Min-Max Theorem
5.1. Monotone Operators in Hilbert Space
5.2. Min-Max Theorem
5.3. Dense Single-Valuedness of Monotone Operators
Chapter 6. Generalized Implicit Function Theorems
6.1. C Smoothing: The Analytic Case
6.2. Analytic Smoothing on Function Spaccs and Analytic Mappings
6.3. C Smoothing and Mapping of Finite Order
6.4. A Theorem or" Kolmogorov, Arnold, and Moser
6.5. Conjugacy Problems
Bibliography
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