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As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear functional analysis. I have tried to close this gap with my five-part lecture notes, the first three parts of which have been published in the Teubner-Texte series by Teubner-Verlag, Leipzig, 1976, 1977, and 1978. The present English edition was translated from a completely rewritten manuscript which is significantly longer than the original version in the Teubner-Texte series. The material is organized in the following way: Part I: Fixed Point Theorems. Part II: Monotone Operators. Part III: Variational Methods and Optimization. Parts IV jV: Applications to Mathematical Physics. The exposition is guided by the following considerations: (a) What are the supporting basic ideas and what intrinsic interrelations exist between them? (/3) In what relation do the basic ideas stand to the known propositions of classical analysis and linear functional analysis? ( y) What typical applications are there? Vll Preface viii Special emphasis is placed on motivation.
- Sales Rank: #3175931 in Books
- Published on: 1984-11-27
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.56" w x 6.14" l, 2.49 pounds
- Binding: Hardcover
- 662 pages
Most helpful customer reviews
8 of 8 people found the following review helpful.
Highly recommended
By Kevin R. Vixie
This is the fourth of E. Zeidler's amazing 5 volume set (I,IIa,IIb,III,IV) on nonlinear functional analysis and it's applications. I am a real fan of these books and have used this particular volume to understand various fine points of variational theory. For example, I very much liked chapter 48 on generalized Lagrange multipliers (Dubovickii-Miljutin theory).
See my review of volume 1 for more extensive comments.
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