Nonlinear functional analysis
Nonlinear functional analysis
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DOI：
10.1007/978-3-662-00547-7
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
K. Deimling
中科院分区：
文献类型：
--
作者：
K. Deimling
主题。然而，只需要适度的初步知识。在第一章中，我们引入了一个重要的拓扑概念，即从Rn的子集到Rn的连续映射的拓扑度，你不需要知道任何泛函分析的知识。从第2章开始，当无限维第一次出现时，人们应该熟悉将一个序列或某种类型的函数视为所有此类序列或函数的相应向量空间中的点的基本步骤，只要这种抽象是值得的。为了便于参考，我们还应该弄清楚在第7节中证明的事情，并接受那里引用的某些线性泛函分析的基本原理，直到它们在后面的章节中应用。换句话说，即使是“完全线性”的部分，我们为了您的方便而包括在内，也只是作为非线性进展的工具。另一点使文本引导性的是使用基本上统一的数学语言和思维方式，这一点无疑是从分析的初级课程中熟悉的，这些课程并不太担心它与代数和拓扑学的联系。当然，我们将使用一些基本的拓扑概念，这些概念可能是新的，但事实上，这里和那里只有几个注释与代数或微分拓扑概念和方法有关。
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.