Methods in Nonlinear Analysis [electronic resource] /by Kung-Ching Chang.
by Chang, Kung-Ching [author.]; SpringerLink (Online service).
Material type:
BookSeries: Springer Monographs in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.Description: IX, 439 p. online resource.ISBN: 9783540292326.Subject(s): Mathematics | Global analysis (Mathematics) | Functional analysis | Differential equations, partial | Mathematical optimization | Mathematics | Analysis | Calculus of Variations and Optimal Control; Optimization | Partial Differential Equations | Functional AnalysisDDC classification: 515 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA299.6-433 (Browse shelf) | Available |
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.
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