经典数学丛书（影印版）：非线性分析方法 [Methods in Nonlinear Analysis] pdf epub mobi txt 电子书 下载 2025

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张恭庆 著

出版社： 世界图书出版公司

ISBN：9787510075933

版次：1

商品编码：11551555

包装：平装

丛书名： 经典数学丛书

外文名称：Methods in Nonlinear Analysis

开本：24开

出版时间：2014-05-01

用纸：胶版纸

页数：439

正文语种：英文

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

评分☆☆☆☆☆

对了，那个客服我真的想给她打个一般，问什么什么不知道，但电话中“2一般”是没办法选的，总提示错误，我只得挂了，这次购物实在太不愉快。上次在京东买了个东西也是个二手的，还有问题，结果寄回去死不承认，最近怎么回事？

评分☆☆☆☆☆

张院士的书籍，非线性分析很好的参考书

评分☆☆☆☆☆

好看(??ω??)??

评分☆☆☆☆☆

有点深啊，要复习了

评分☆☆☆☆☆

还行

评分☆☆☆☆☆

值得学习的一本书

评分☆☆☆☆☆

看着还不错看着还不错

评分☆☆☆☆☆

给客服打电话联系，客服一问三不知，总让我等等，电话打了10分钟，最后换还要垫付邮费，自己跑腿，各种麻烦，反正几十块，自己认倒霉吧。以后开发票麻烦把金额和类别写清楚再开好吗？？？？

评分☆☆☆☆☆

早就想入手，赶上促销，速度买。价格很低了