Methods in Nonlinear Analysis by Chang, Kung-Ching;

Sorozatcím: Springer Monographs in Mathematics;

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A termék adatai:

Kiadás sorszáma 2005
Kiadó Springer Berlin Heidelberg
Megjelenés dátuma 2010. október 21.
Kötetek száma 1 pieces, Previously published in hardcover

ISBN 9783642063275
Kötéstípus Puhakötés
Lásd még 9783540241331
Terjedelem442 oldal
Méret 235x155 mm
Súly 688 g
Nyelv angol
Illusztrációk X, 442 p. Illustrations, black & white

Kategóriák

Analízis Optimalizáció, lineáris programozás, játékelmélet Matematika a mérnöki- és természettudományok területén Analízis (karitatív célú kampány) Optimalizáció, lineáris programozás, játékelmélet (karitatív célú kampány) Matematika a mérnöki- és természettudományok területén (karitatív célú kampány)

Hosszú leírás:

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 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.

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. Topics covered include linearization, fixed-point theorems based on compactness and convexity, topological degree theory, minimization and topological variational methods. 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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