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内容简介

　　Many nonlinear analysis problems have their roots in geometry，astronomy，fluid and elastic mechanics，physics，chemistry，biology，control theory，image processing and economics. The theories and methods in nonlinear analysis stem from many areas of mathematics： Ordinary drfferential equations，partial differential equations，the calculus of variations，dynamical systems，differential geometry，Lie groups，algebraic topology，linear and nonlinear functional analysis，measure theory，harmonic analysis，convex analysis，game theory，optimization theory，etc. Amidst solving these problems，many branches are intertwined，thereby advancing each other.
　　The book is the result of many years of revision of the author's lecture notes. Some of the more involved sections were originally used in seminars as introductory parts of some new subjects. However，due to their importance，the materials have been reorganized and supplemented，so that they may be more valuable to the readers.

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目录

1 Linearization
1.1 Differential Calculus in Banach Spaces
1.1.1 Frechet Derivatives and Gateaux Derivatives
1.1.2 Nemytscki Operator
1.1.3 High-Order Derivatives
1.2 Implicit Function Theorem and Continuity Method
1.2.1 Inverse Function Theorem
1.2.2 Applications
1.2.3 Continuity Method
1.3 Lyapunov-Schmidt Reduction and Bifurcation
1.3.1 Bifurcation
1.3.2 Lyapunov-Schmidt Reduction
1.3.3 A Perturbation Problem
1.3.4 Gluing
1.3.5 Transversality
1.4 Hard Implicit Function Theorem
1.4.1 The Small Divisor Problem
1.4.2 Nash-Moser Iteration

2 Fixed-Point Theorems
2.1 Order Method
2.2 Convex Function and Its Subdifferentials
2.2.1 Convex Functions
2.2.2 Subdifferentials
2.3 Convexity and Compactness
2.4 Nonexpansive Maps
2.5 Monotone Mappings
2.6 Maximal Monotone Mapping

3 Degree Theory and Applications
3.1 The Notion of Topological Degree
3.2 Fundamental Properties and Calculations of Brouwer Degrees
3.3 Applications of Brouwer Degree
3.3.1 Brouwer Fixed-Point Theorem
3.3.2 The Borsuk-Ulam Theorem and Its Consequences
3.3.3 Degrees for Sl Equivariant Mappings
3.3.4 Intersection
3.4 Leray-Schauder Degrees
3.5 The Global Bifurcation
3.6 Applications
3.6.1 Degree Theory on Closed Convex Sets ,
3.6.2 Positive Solutions and the Scaling Method
3.6.3 Krein-Rutman Theory for Positive Linear Operators
3.6.4 Multiple Solutions
3.6.5 A Free Boundary Problem
3.6.6 Bridging
3.7 Extensions
3.7.1 Set-Valued Mappings
3.7.2 Strict Set Contraction Mappings and Condensing Mappings
3.7.3 Fredholm Mappings

4 Minimization Methods
4.1 Variational Principles
4.1.1 Constraint Problems
4.1.2 Euler-Lagrange Equation
4.1.3 Dual Variational Principle
4.2 Direct Method
4.2.1 Fundamental Principle
4.2.2 Examples
4.2.3 The Prescribing Gaussian Curvature Problem and the Schwarz Symmetric Rearrangement
4.3 Quasi-Convexity
4.3.1 Weak Continuity and Quasi-Convexity
4.3.2 Morrey Theorem
4.3.3 Nonlinear Elasticity
4.4 Relaxation and Young Measure
4.4.1 Relaxations
4.4.2 Young Measure
4.5 Other Function Spaces
4.5.1 BV Space
4.5.2 Hardy Space and BMO Space
4.5.3 Compensation Compactness
4.5.4 Applications to the Calculus of Variations
……
5 Topological and Variational Methods
Notes
References

前言/序言

经典数学丛书（影印版）：非线性分析方法 [Methods in Nonlinear Analysis] 电子书 下载 mobi epub pdf txt

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张老师的名作,准备拜读下

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好看(??ω??)??

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一如既往好。

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数学专业学习好。有教育意义的书籍，推荐给大家分享了吧

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专业

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搜了下，评价貌似不错，买了

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经典的教材，京东活动时购买的，很喜欢。

评分☆☆☆☆☆

很好的一本书，很有帮助

评分☆☆☆☆☆

挺好的。。。。。。。

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