A Topological Introduction to Nonlinear Analysis / Edition 2 available in Paperback
- Pub. Date:
- Birkhï¿½user Boston
"The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory . . . reading is fluid and very pleasant . . . style is informal but far from being imprecise."
—MATHEMATICAL REVIEWS (Review of the First Edition)
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 ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world.
New to the second edition: New chapters will supply additional applications of the theory and techniques presented in the book.
• Several new proofs, making the second edition more self-contained.
|Edition description:||2nd ed. 2004|
|Product dimensions:||6.10(w) x 9.25(h) x 0.36(d)|
About the Author
Table of Contents
Preface.- Part I 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 Bernstain Theory.- Part II 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.- Part III Fixed Point Index Theory.- A Retraction Theorum.- The Fixed Point Index.- The Tubulur Reactor.- Fixed Points in a Cone.- Eigenvalues and Eigenvectors.- Part IV Bifurcation Theory.- A Separation Theorem.- Compact Linear Operators.- The Degree Calculation.- The Krasnoselskii-Rabinowitz Theorem.- Nonlinear Strum Liouville Theory.- More Strum Liouville Theory.- Euler Buckling.- Part V Appendices.