点击选择搜索分类
首页 - 科普读物- 正文
☆☆☆☆☆
||
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
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.
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
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
经典数学丛书(影印版):非线性分析方法 [Methods in Nonlinear Analysis]-so88
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 2022
图书介绍
☆☆☆☆☆
||
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.
内页插图
目录
1 Linearization1.1 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
电子书下载地址:
相关电子书推荐:
- 文件名
- 世界是通的:“一带一路”的逻辑(英) 9787508536262 王义栀-RT
- 稻谷加工工艺与设备 阮少兰 刘洁 高等院校粮食工程教材书籍
- 中侨大讲堂:中外人文大讲堂
- 胡乐国盆景作品(精)
- {RT}神秘的西域-齐浩然著 金盾出版社 9787508291963
- 张竹邦说翡翠:翡翠秘史
- 毁灭者 9787533176488
- 宠物萌萌哒(宠物逸闻趣事)
- 当代弗兰肯斯坦:误入歧途的现代科学
- 精选客厅设计及材料解析:大户型客厅
- 介绍丛书:混沌学
- 奶牛健康养殖技术
- 科学平行(2017) 9787504674678
- 中国观赏园艺研究进展:2017:2017 9787503892110
- 恒星运动和宇宙结构 9787535290212