經典數學叢書（影印版）：非綫性分析方法 [Methods in Nonlinear Analysis] 下載 mobi epub pdf 電子書 2025

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☆☆☆☆☆

張恭慶 著

齣版社： 世界圖書齣版公司

ISBN：9787510075933

版次：1

商品編碼：11551555

包裝：平裝

叢書名： 經典數學叢書

外文名稱：Methods in Nonlinear Analysis

開本：24開

齣版時間：2014-05-01

用紙：膠版紙

頁數：439

正文語種：英文

內容簡介

　　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.

內頁插圖

目錄

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

評分☆☆☆☆☆

有點深啊，要復習瞭

評分☆☆☆☆☆

看著還不錯看著還不錯

評分☆☆☆☆☆

專業書，原版太貴，隻能這樣

評分☆☆☆☆☆

給客服打電話聯係，客服一問三不知，總讓我等等，電話打瞭10分鍾，最後換還要墊付郵費，自己跑腿，各種麻煩，反正幾十塊，自己認倒黴吧。以後開發票麻煩把金額和類彆寫清楚再開好嗎？？？？

評分☆☆☆☆☆

為何沒人告訴我，書的內容純英文的，除瞭封麵有幾個漢子，誰有時間讀這樣一本純英文的書

評分☆☆☆☆☆

好書，好書，我很喜歡看。

評分☆☆☆☆☆

經典專業書籍，多次購買，質量一如既往。

評分☆☆☆☆☆

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.

評分☆☆☆☆☆

很好的一本書，很有幫助