Nonlinear Functional Analysis

This book mainly provides the basic theories and methods of nonlinear functional analysis. The content includes Fréchet differentiation, the implicit function theorem, bifurcation problems, Brouwer degree, Leray-Schauder degree, fixed point theorems, topological degree of cone mappings, the global bifurcation theorem, extremum principles, Ekeland's variational principle, the minimax principle, index, and category.It consists of three chapters: Nonlinear Operators on Banach Spaces, Topological Degree Theory, and Variational Methods. Some examples are given to explain the applications of these theories, and each chapter contains exercises.This is a textbook for graduate students and senior undergraduate students.