Differentiable operators and nonlinear equations
The need to study holomorphic mappings in infinite dimensional spaces, in all likelihood, arose for the first time in connection with the development of nonlinear analysis. A systematic study of integral equations with an analytic nonlinear part was started at the end of the 19th and the beginning of the 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the m…
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- Full title :Differentiable operators and nonlinear equations / Victor Khatskevich, David Shoiykhet ; translated from the Russian by Mircea Martin.
Summary
The need to study holomorphic mappings in infinite dimensional spaces, in all likelihood, arose for the first time in connection with the development of nonlinear analysis. A systematic study of integral equations with an analytic nonlinear part was started at the end of the 19th and the beginning of the 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods, which subsequently have been refined and developed. Parallel with these achievements, the theory of functions of one or several complex variables was gradually enriched with more significant and subtle results. The present book is a first step towards establishing a bridge between nonlinear analysis, nonlinear operator equations and the theory of holomorphic mappings on Banach spaces. The work concludes with a brief exposition of the theory of spaces with indefinite metrics, and some relevant applications of the holomorphic mappings theory in this setting. In order to make this book accessible not only to specialists but also to students and engineers, the authors give a complete account of definitions and proofs, and also present relevant prerequisites from functional analysis and topology. Contents: Preliminaries " Differential calculus in normed spaces " Integration in normed spaces " Holomorphic (analytic) operators and vector-functions on complex Banach spaces " Linear operators " Nonlinear equations with differentiable operators " Nonlinear equations with holomorphic operators " Banach manifolds " Non-regular solutions of nonlinear equations " Operators on spaces with indefinite metric " References " List of Symbols " Subject Index
Read More ↓Edition Statements
- Publication Date:©1994.
Publication Statements
- Publisher(s):Birkhäuser Verlag
- Place of Publication:Basel
- Language:eng
- Publication Date:©1994.
The Physical Object
- Description:1 online resource (x, 280 pages) : : illustrations
Edition Identifiers
- ISBN:9783034896580, 3034896581, 9783034885126, 3034885121
- oclc:ocn810356399
- LC Classification:QA613.64
- Dewey Decimal:514/.72
Table of Contents
Ch. 0. Preliminaries -- Ch. I. Differential calculus in normed spaces -- Ch. II. Integration in normed spaces -- Ch. III. Holomorphic (analytic) operators and vector-functions on complex Banach spaces -- Ch. IV. Linear operators -- Ch. V. Nonlinear equations with differentiable operators -- Ch. VI. Nonlinear equations with holomorphic operators -- Ch. VII. Banach manifolds -- Ch. VIII. Non-regular solutions of nonlinear equations -- Ch. IX. Operators on spaces with indefinite metric.
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