Geometrical Methods in Variational Problems / by N. A. Bobylev, S. V. Emel’yanov, S. K. Korovin
(Mathematics and Its Applications ; 485)
| データ種別 | 電子ブック |
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| 出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
| 出版年 | 1999 |
| 本文言語 | 英語 |
| 大きさ | XVI, 543 p : online resource |
書誌詳細を非表示
| 内容注記 | 1 Preliminaries 1.1 Metric and Normed Spaces 1.2 Compactness 1.3 Linear Functional and Dual Spaces 1.4 Linear Operators 1.5 Nonlinear Operators and Functionals 1.6 Contraction Mapping Principle, Implicit Function Theorem, and Differential Equations on a Banach Space 2 Minimization of Nonlinear Functionals 2.1 Extrema of Smooth Functionals 2.2 Extremum of Lipschitzian and Convex Functionals 2.3 Weierstass Theorems 2.4 Monotonicity 2.5 Variational Principles 2.6 Additional Remarks 3 Homotopic Methods in Variational Problems 3.1 Deformations of Functionals on Hilbert Spaces 3.2 Deformations of Functionals on Banach Spaces 3.3 Global Deformations of Functionals 3.4 Deformation of Problems of the Calculus of Variations 3.5 Deformations of Lipschitzian Functions 3.6 Global Deformations of Lipschitzian Functions 3.7 Deformations of Mathematical Programming Problems 3.8 Deformations of Lipschitzian Functionals 3.9 Additional Remarks 4 Topological Characteristics of Extremals of Variational Problems 4.1 Smooth Manifolds and Differential Forms 4.2 Degree of Mapping 4.3 Rotation of Vector Fields in Finite-Dimensional Spaces 4.4 Vector Fields in Infinite-Dimensional Spaces 4.5 Computation of the Topological Index 4.6 Topological Index of Zero of an Isolated Minimum 4.7 Euler Characteristic and the Topological Index of an Isolated Critical Set 4.8 Topological Index of Extremals of Problems of the Calculus of Variations 4.9 Topological Index of Optimal Controls 4.10 Topological Characteristic s of Critical Points of Nonsmooth Functionals 4.11 Additional Remarks 5 Applications 5.1 Existence Theorems 5.2 Bounds of the Number of Solutions to Variational Problems 5.3 Applications of the Homotopic Method 5.4 Study of Degenerate Extremals 5.5 Morse Lemmas 5.6 Well-Posedness of Variational Problems. Ulam Problem 5.7 Gradient Procedures 5.8 Bifurcation of Extremals of Variational Problems 5.9 Eigenvalues of Potential Operators 5.10 Additional Remarks Bibliographical Comments References |
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| 著者標目 | *Bobylev, N. A. author Emel’yanov, S. V. author Korovin, S. K. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Differential equations LCSH:Partial differential equations LCSH:Mathematical optimization LCSH:Calculus of variations FREE:Mathematics FREE:Calculus of Variations and Optimal Control; Optimization FREE:Optimization FREE:Global Analysis and Analysis on Manifolds FREE:Partial Differential Equations FREE:Ordinary Differential Equations |
| 分 類 | DC23:515.64 |
| 巻冊次 | ISBN:9789401146296 
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| ISBN | 9789401146296 |
| URL | http://dx.doi.org/10.1007/978-94-011-4629-6 |
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