●1 Function Spaces
1.1 Introduction
1.1.1 LP-Spaces
1.1.2 Lebesgue-Bochner Spaces
1.1.3 BV-Functions，Absolutely Continuous Functions，Spaces of Measures
1.1.4 Sobolev Spaces
1.1.5 Auxiliary Notions
1.2 Problems
1.3 Solutions
Bibliography
2 Nonlinear and ltivalued Maps
2.1 Introduction
2.1.1 Compact，Completely Continuous，and Proper Maps
2.1.2 ltifunctions
2.1.3 Maximal Monotone Maps and Generalizations
2.1.4 Accretive Maps
2.1.5 Miscellaneous Results
2.2 Problems
2.3 Solutions
Bibliography
3 Smooth and Nonsmooth Calculus
3.1 Introduction
3.1.1 Gateaux and Frechet Derivatives
3.1.2 Convex Functionals and Variational Inequalities
3.1.3 Locally Lipschitz Functions
3.1.4 г-Convergence and Relaxation
3.2 Problems
3.3 Solutions
Bibliography
4 Degree Theory and Fixed Point Theory
4.1 Introduction
4.1.1 Degree Theory
4.1.2 Metric Fixed Point Theory
4.1.3 Topological Fixed Point Theory
4.1.4 Order Fixed Point Theory
4.2 Problems
4.3 Solutions
Bibliography
5 Variational and Topological Methods
5.1 IIltroduction
5.1.1 Minimization Methods
5.1.2 Minimax Methods for Critical Points
5.1.3 Morse Theory：Critical Groups
5.1.4 Dirichlet Elliptic Problems
5.2 Problems
5.3 Solutions
Bibliography
List of Symbols
Index
編輯手記

本書研究的主題涵蓋了非線性分析的大部分內容，共分為五部分：第一部分介紹了函數空間；第二部分給出了非線性和多值映射的相關內容；第三部分闡述了光滑與非光滑微積分的相關理論；第四部分論述了拓撲度理論和不動點理論；第五部分介紹了變分和拓撲方法，不僅給出了相關的定義和結果，還闡述了有關概念和結果的注釋和評論，約有200個問題及其解決方案，可以幫助讀者在解決問題之前掌握其理論知識。本書適合大學師生及數學愛好者參考閱讀。