AuthorBrown, Robert F. author
TitleA Topological Introduction to Nonlinear Analysis [electronic resource] / by Robert F. Brown
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1993
Connect tohttp://dx.doi.org/10.1007/978-1-4757-1209-4
Descript IX, 146 p. 23 illus. online resource

SUMMARY

Nonlinear analysis is a remarkable mixture of topology, analysis and applied mathematics. Mathematicians have good reason to become acquainted with this important, rapidly developing subject. But it is a BIG subject. You can feel it: just hold Eberhard Zeidler's Nonlinear Functional Analysis and Its Applications I: Fixed Point Theorems [Z} in your hand. It's heavy, as a 900 page book must be. Yet this is no encyclopedia; the preface accurately describes the " ... very careful selection of material ... " it contains. And what you are holding is only Part I of a five-part work. So how do you get started learning nonlinear analysis? Zeidler's book has a first page, and some people are quite comfortable beginning right there. For an alternative, the bibliography in [Z], which is 42 pages long, contains exposition as well as research results: monographs that explain portions of the subject to a variety of audiences. In particular, [D} covers much of the material of Zeidler's book. What makes this book different? The answer is in three parts: this book is (i) topological (ii) goal-oriented and (iii) a model of its subject


CONTENT

I: Fixed Point Existence Theory -- 1. The Topological Point of View -- 2. Ascoli-Arzela Theory -- 3. Brouwer Fixed Point Theory -- 4. Schauder Fixed Point Theory -- 5. Equilibrium Heat Distribution -- 6. Generalized Bernstein Theory -- II: Degree and Bifurcation -- 7. Some Topological Background -- 8. Brouwer Degree -- 9. Leray-Schauder Degree -- 10. Properties of the Leray-Schauder Degree -- 11. A Separation Theorem -- 12. Compact Linear Operators -- 13. The Degree Calculation -- 14. The Krasnoselskii-Rabinowitz Bifurcation Theorem -- 15. Nonlinear Sturm-Liouville Theory -- 16. Euler Buckling -- Appendices -- A. Singular Homology -- B. Additivity and Product Properties -- References


SUBJECT

  1. Mathematics
  2. Functional analysis
  3. Differential equations
  4. Partial differential equations
  5. Topology
  6. Mathematics
  7. Functional Analysis
  8. Ordinary Differential Equations
  9. Partial Differential Equations
  10. Topology