Nonlinear analysis shows the basic theory, methods, skills and results of dealing with nonlinear problems from a mathematical point of view. Its purpose is to provide an introductory book on nonlinear analysis for graduate students majoring in mathematics and related fields. This book pays attention to the background and source of the problem, highlights the core idea of solving the problem, refines the details and is concise. This book is compiled according to the author's handouts to master students and doctoral students in the Department of Mathematics of Harbin Institute of Technology. Combined with the teaching practice in recent five years and considering the basic needs of graduate students, the contents of this book have been sorted out and carefully selected, covering a comprehensive and focused way, with both theoretical depth and the application of methods and skills in typical models, hoping to help readers who read this book.

Nonlinear analysis is the basic theoretical textbook of nonlinear analysis, including topological degree theory and its application, convex analysis and optimization, monotone operator theory, variational and critical point theory, and bifurcation theory. This book pays attention to the background of the problem, the theory is concise and easy to understand, the content is carefully selected, and there are appropriate exercises at the end of each chapter to facilitate readers to read and consolidate.