Nonlinear Analysis and Semilinear Elliptic Problems
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Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A series of Appendices give convenient accounts of a variety of advanced topics that will introduce the reader to areas of current research. The book is amply illustrated and many chapters are rounded off with a set of exercises.Read more
- Contains both classical and more modern advanced techniques and is an ideal introduction to Nonlinear Analysis
- Ideal for graduate students and academic researchers in Mathematics and Physics
- Series of Appendices introduces reader to advanced areas of current research
- Discusses both topological and variational tools
Reviews & endorsements
'In the reviewer's opinion, this book can serve very well as a textbook in topological and variational methods in nonlinear analysis. Even researchers working in this field might find some interesting material (at least the reviewer did).' Zentralblatt MATH
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- Date Published: March 2007
- format: Adobe eBook Reader
- isbn: 9780511266744
- contains: 55 b/w illus. 28 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
Part I. Topological Methods:
2. A primer on bifurcation theory
3. Topological degree, I
4. Topological degree, II: global properties
Part II. Variational Methods, I:
5. Critical points: extrema
6. Constrained critical points
7. Deformations and the Palais-Smale condition
8. Saddle points and min-max methods
Part III. Variational Methods, II:
9. Lusternik-Schnirelman theory
10. Critical points of even functionals on symmetric manifolds
11. Further results on Elliptic Dirichlet problems
12. Morse theory
Part IV. Appendices: Appendix 1. Qualitative results
Appendix 2. The concentration compactness principle
Appendix 3. Bifurcation for problems on Rn
Appendix 4. Vortex rings in an ideal fluid
Appendix 5. Perturbation methods
Appendix 6. Some problems arising in differential geometry
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