A topological introduction to nonlinear analysis / Robert F. Brown.
Here is a book that will be a joy to the mathematician or graduate student of mathematics or even the well-prepared undergraduate who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded...
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Full Text (via Springer) |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boston :
Birkhäuser,
©2004.
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| Edition: | 2nd ed. |
| Subjects: |
Table of Contents:
- Fixed point existence theory. The topological point of view ; Ascoli-arzela theory ; Brouwer fixed point theory ; Schauder fixed point theory ; The forced pendulum ; Equilibrium heat distribution ; Generalized Bernstein theory
- Degree theory. Brouwer degree ; Properties of the Brouwer Degree ; Leray-Schauder degree ; Properties of the Leray-Schauder Degree ; The Mawhin operator ; The pendulum swings back
- Bifurcation theory. A separation theorem ; Compact linear operators ; The degree calculation ; The Krasnoselskii-Rabinowitz bifurcation theorem ; Nonlinear Sturm-Liouville theory ; More Sturm-Liouville theory ; Euler buckling
- Appendices. Singular homology ; Additivity and product properties ; Bounded linear transformations.