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

目录
- 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