Nonlinear Functional Analysis pdf epub mobi txt 电子书 下载 2025
- Nonlinear_Functional_Analysis
- Mathematics
- 非线性泛函分析
- 泛函分析
- 数学分析
- 高等数学
- 拓扑学
- 优化
- 变分法
- 偏微分方程
- 数值分析
- 应用数学
具体描述
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical language and way of thinking, one which is no doubt familiar from elementary lectures in analysis that did not worry much about its connections with algebra and topology. Of course we shall use some elementary topological concepts, which may be new, but in fact only a few remarks here and there pertain to algebraic or differential topological concepts and methods.
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目录信息
Pages I-XIV
Topological Degree in Finite Dimensions
Klaus Deimling
Pages 1-34
Topological Degree in Infinite Dimensions
Klaus Deimling
Pages 35-94
Monotone and Accretive Operators
Klaus Deimling
Pages 95-145
Implicit Functions and Problems at Resonance
Klaus Deimling
Pages 146-185
Fixed Point Theory
Klaus Deimling
Pages 186-216
Solutions in Cones
Klaus Deimling
Pages 217-255
Approximate Solutions
Klaus Deimling
Pages 256-277
Multis
Klaus Deimling
Pages 278-318
Extremal Problems
Klaus Deimling
Pages 319-377
Bifurcation
Klaus Deimling
Pages 378-425
Epilogue
Klaus Deimling
Pages 426-427
Back Matter
Pages 428-452
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