Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
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DOI：
10.1007/978-1-4612-0981-2
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发表时间：
1988-03
期刊：
影响因子：
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通讯作者：
E. Zeidler
中科院分区：
文献类型：
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作者：
E. Zeidler
这是第二个五卷阐述的主要原则的非线性泛函分析及其应用的自然科学，经济学和数值分析。演示文稿是独立的，非专业人士也可以访问。第二部分是关于单调算子的理论。它分为两个分卷，二/A和二/B，构成一个单元。本部分II/A是专门用于线性单调算子。它作为一个基本的介绍现代功能分析处理变分问题，积分方程，偏微分方程的椭圆，抛物和双曲型。这本书还介绍了数值泛函分析与应用程序的里兹方法沿着与方法的有限元，伽辽金法，和差分法。许多练习是对课文的补充。单调算子理论与希尔伯特对狄利克雷原理的严格证明以及希尔伯特在1900年著名的巴黎演讲中提出的第19和第20个问题密切相关，这些问题强烈影响了世纪分析的发展。
This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.