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Methods in Nonlinear Analysis / by Kung-Ching Chang
(Springer Monographs in Mathematics. ISSN:21969922)
版 | 1st ed. 2005. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 2005 |
本文言語 | 英語 |
大きさ | X, 442 p : online resource |
著者標目 | *Chang, Kung-Ching author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Differential equations LCSH:Functional analysis FREE:Analysis FREE:Calculus of Variations and Optimization FREE:Differential Equations FREE:Functional Analysis |
一般注記 | Linearization -- Fixed-Point Theorems -- Degree Theory and Applications -- Minimization Methods -- Topological and Variational Methods Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials scattered throughout the literature from the methodology point of view, and presents them in a systematic way. It contains the basic theories and methods with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. There are five chapters that cover linearization, fixed-point theorems based on compactness and convexity, topological degree theory, minimization and topological variational methods. Each chapter combines abstract, classical and applied analysis. Particular topics included are bifurcation, perturbation, gluing technique, transversality, Nash–Moser technique, Ky Fan's inequality and Nash equilibrium in game theory, setvalued mappings and differential equations with discontinuous nonlinear terms, multiple solutions in partial differential equations, direct method, quasiconvexity and relaxation, Young measure, compensation compactness method and Hardy space, concentration compactness and best constants, Ekeland variational principle, infinite-dimensional Morse theory, minimax method, index theory with group action, and Conley index theory. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry. The book aims to find a balance between theory and applications and will contribute to filling the gap between texts that either only study the abstract theory, or focus on some special equations HTTP:URL=https://doi.org/10.1007/3-540-29232-2 |
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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 | 9783540292326 |
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EB00232150 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000134142 |
ISBN | 9783540292326 |
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※2017年9月4日以降