非线性泛函分析专题（影印版）

样章

作者：

Louis Nirenberg，Ralph A. Artino

定价：

99.00 元

版面字数：

240.00千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-063098-5

物料号：

63098-00

出版时间：

2025-02-14

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

前辅文
Preface to New Edition
Preface
Chapter 1.Topological Approach: Finite Dimensions
- 1.1.A Simple Remark
- 1.2.Sard's Theorem
- 1.3.Finite-Dimensional Degree Theory
- 1.4.Properties of Degree
- 1.5.Further Properties and Remarks
- 1.6.Some Applications to Nonlinear Equations
- 1.7.Borsuk's Theorem
- 1.8.Mappings in Different Dimensions
Chapter 2.Topological Degree in Banach Space
- 2.1.Schauder Fixed-Point Theorem
- 2.2.An Application
- 2.3.Leray-Schauder Degree
- 2.4.Some Compact Operators
- 2.5.Elliptic Partial Differential Equations
- 2.6.Mildly Nonlinear Perturbations of Linear Operators
- 2.7.Calculus in Banach Space
- 2.8.The Leray-Schauder Degree for Isolated Solutions, the Index
Chapter 3.Bifurcation Theory
- 3.1.The Morse Lemma
- 3.2.Application of the Morse Lemma
- 3.3.Krasnoselski's Theorem
- 3.4.A Theorem of Rabinowitz
- 3.5.Extension of Krasnoselski’s Theorem
- 3.6.Stability of Solutions
- 3.7.The Number of Global Solutions of a Nonlinear Problem
Chapter 4.Further Topological Methods
- 4.1.Extension of Leray-Schauder Degree
- 4.2.Applications to Partial Differential Equations
- 4.3.Framed Cobordism
- 4.4.Stable Cohomotopy Theorem
- 4.5.Cohomotopy Groups
- 4.6.Stable Cohomotopy Theory
- 4.7.Application to Existence of Global Solutions
Chapter 5.Monotone Operators and the Min-Max Theorem
- 5.1.Monotone Operators in Hilbert Space
- 5.2.Min-Max Theorem
- 5.3.Dense Single-Valuedness of Monotone Operators
Chapter 6.Generalized Implicit Function Theorems
- 6.1.Cω Smoothing: The Analytic Case
- 6.2.Analytic Smoothing on Function Spaces and Analytic Mappings
- 6.3.C∞ Smoothing and Mapping of Finite Order
- 6.4.A Theorem of Kolmogorov, Arnold, and Moser
- 6.5.Conjugacy Problems
Bibliography