- 非线性泛函分析专题(英文版)(精)/美国数学会经典影印系列
- - 作者：(美)路易斯·尼伦伯格//拉尔夫·A.阿蒂诺|责编:李华英
  - 出版社：高等教育
  - ISBN：9787040630985
  - 出版日期：2025/02/01
  - 页数：145
- 售价：39.6

内容大纲
本书发展了处理非线性常微分方程和偏微分方程的拓扑和解析方法。本书适合对泛函分析感兴趣的研究生和数学研究人员阅读参考。
作者介绍
目录
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 l.inear 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.  C Smoothing: The Analytic Case
  6.2.  Analytic Smoothing on Function Spaccs and Analytic Mappings
  6.3.  C Smoothing and Mapping of Finite Order
  6.4.  A Theorem or" Kolmogorov, Arnold, and Moser
  6.5.  Conjugacy Problems
Bibliography

内容大纲

作者介绍

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