Methods in Nonlinear Analysis

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.