A topological introduction to nonlinear analysis
著者
書誌事項
A topological introduction to nonlinear analysis
Birkhäuser, c1993
- : us : pbk
- : sz : pbk
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注記
Includes bibliographical references (p. [144]) and index
内容説明・目次
内容説明
Here is a book that will be a joy to the mathematician or graduate student of mathematics - or even wen prep 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 0 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 characterise our real world. A classical example is given in the differential equation problem that models the maximum weight a column can support without buckling. The author has assumed a fairly high level of mathematical sophistication. However, the pace of the exposition is relatively leisurely, and the book is essentially self-contained. Upon completing the book, the reader will be wen equipped to make rapid progress through the existing literature in the broad field of nonlinear analysis.
This book is highly recommended for self study for mathematicians and students interested in such areas as geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practising topologist who has seen a clear path to understanding.
目次
Part 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 Part 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 Theorem 15. Nonlinear Sturm-Liouville Theory 16. Euler Buckling Appendices A. Singular Homology B. Additivity and Product Properties References Index
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