Methods in Nonlinear Analysis

  • Kung-Ching Chang

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Pages 1-70
  3. Pages 71-126
  4. Pages 205-314
  5. Back Matter
    Pages 419-439

About this book


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.


Convexity Hardy space Morse Theory Nonlinear Partial Differential Equations Nonlinear analysis Nonlinear functional analysis calculus compactness differential equation fixed-point theorem measure minimum ordinary differential equation partial

Authors and affiliations

  • Kung-Ching Chang
    • 1
  1. 1.School of Mathematical Sciences Peking UniversityBeijingPeople's Republic of China

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