新書推薦:

《
存在的意义 11位心理治疗师的存在-人本之旅(孤独、意义、自由、敬畏、死亡交织在人生旅途中,推动我们
》
售價:NT$
434

《
达尔文的植物世界 跟随达尔文的试验与研究发现自然植物的奥秘 达尔文进化论植物篇
》
售價:NT$
765

《
从世界工厂到世界引擎:中国创新的黄金时代2015-2025
》
售價:NT$
347

《
你永远有选择
》
售價:NT$
265

《
1848变革之年(理想,是“民族之春”,现实,是“血色夏日”,革命风暴席卷欧洲,旧时代的丧钟为新秩序
》
售價:NT$
398

《
拓客销售:可持续的营收增长
》
售價:NT$
352

《
骨与肉
》
售價:NT$
286

《
联结思维
》
售價:NT$
352
|
| 內容簡介: |
|
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。Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book has served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references.Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitzs global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems.After more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text.
|
|