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Methods in Nonlinear Analysis

  • Kartonierter Einband
  • 452 Seiten
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Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques and results in many different branches of... Weiterlesen
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Beschreibung

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, NashMoser 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.



Collects and reorganizes up-to-date materials scattered throughout the literature, and presents them in a systematic way

Includes basic material as well as modern developments

Chapters cover linearization; fixed-point theorems based on compactness and convexity; topological degree theory; minimization and topological variational methods



Inhalt
Linearization.- Fixed-Point Theorems.- Degree Theory and Applications.- Minimization Methods.- Topological and Variational Methods.

Produktinformationen

Titel: Methods in Nonlinear Analysis
Autor:
EAN: 9783642063275
ISBN: 3642063276
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Genre: Mathematik
Anzahl Seiten: 452
Gewicht: 680g
Größe: H235mm x B155mm x T24mm
Jahr: 2010
Auflage: Softcover reprint of hardcover 1st ed. 2005

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