Rong Yuan

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.

This book is composed of lecture notes on courses to graduate students at various universities on the asymptotic behaviour of differential equations. Anyone who has some acquaintance with differential equations in Banach spaces and Functional Analysis can read this book. It is primarily intended for graduate students and beginning researchers in the theory of evolution equations.