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A Topological Introduction to Nonlinear Analysis / by Robert F. Brown
版 | 1st ed. 1993. |
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出版者 | (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser) |
出版年 | 1993 |
本文言語 | 英語 |
大きさ | IX, 146 p. 23 illus : online resource |
著者標目 | *Brown, Robert F author SpringerLink (Online service) |
件 名 | LCSH:Functional analysis LCSH:Differential equations LCSH:Topology FREE:Functional Analysis FREE:Differential Equations FREE:Topology |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-1-4757-1209-4 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781475712094 |
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EB00231492 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA319-329.9 DC23:515.7 |
書誌ID | 4000106738 |
ISBN | 9781475712094 |
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