Nonlinear Functional Analysis
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, wh...
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1985, 1985
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| Edition: | 1st ed. 1985 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Topological Degree in Finite Dimensions
- § 1. Uniqueness of the Degree
- § 2. Construction of the Degree
- § 3. Further Properties of the Degree
- § 4. Borsuk’s Theorem
- § 5. The Product Formula
- § 6. Concluding Remarks
- 2. Topological Degree in Infinite Dimensions
- § 7. Basic Facts About Banach Spaces
- § 8. Compact Maps
- § 9. Set Contractions
- § 10. Concluding Remarks
- 3. Monotone and Accretive Operators
- § 11. Monotone Operators on Hilbert Spaces
- § 12. Monotone Operators on Banach Spaces
- § 13. Accretive Operators
- § 14. Concluding Remarks
- Exercises
- 4. Implicit Functions and Problems at Resonance
- § 15. Implicit Functions
- § 16. Problems at Resonance
- 5. Fixed Point Theory
- § 17. Metric Fixed Point Theory
- § 18. Fixed Point Theorems Involving Compactness
- 6. Solutions in Cones
- § 19. Cones and Increasing Maps
- § 20. Solutions in Cones
- 7. Approximate Solutions
- § 21. Approximation Solvability
- § 22. A-Proper Maps and Galerkin for Differential Equations
- 8. Multis
- § 23. Monotone and Accretive Multis
- § 24. Multis and Compactness
- 9. Extremal Problems
- § 25. Convex Analysis
- § 26. Extrema Under Constraints
- § 27. Critical Points of Functionals
- 10. Bifurcation
- § 28. Local Bifurcation
- § 29. Global Bifurcation
- § 30. Further Topics in Bifurcation Theory
- Epilogue
- Symbols