经典数学丛书（影印版）：非线性分析方法 [Methods in Nonlinear Analysis] epub pdf mobi txt 电子书 下载 2024

经典数学丛书（影印版）：非线性分析方法 [Methods in Nonlinear Analysis] epub pdf mobi txt 电子书 下载 2024

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经典数学丛书（影印版）：非线性分析方法 [Methods in Nonlinear Analysis] epub pdf mobi txt 电子书 下载 2024

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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.

内页插图

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] epub pdf mobi txt 电子书 下载 2024

经典数学丛书（影印版）：非线性分析方法 [Methods in Nonlinear Analysis] 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

收藏书！

评分☆☆☆☆☆

张恭庆院士的专著，推荐给数学专业人士！

评分☆☆☆☆☆

包装还行，活动时买的。还没看，先收藏。

评分☆☆☆☆☆

曾经买过英文原版的，北大张院士的专著，如今有了影印本，好。

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书脊有损坏，内容与商家无关

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经典书籍，到货很快

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很好的一本书，很有帮助

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最近恶补数学，工作了发现数学太重要了

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数没包装太好。开的发票上印得特别不清楚，完全没办法报销。

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