戻る / Previous page

Series : Advances in Mechanics and Mathematics

Handbook of Applied Analysis

Handbook of Applied Analysis
Author
Papageorgiou, Nikolaos S./ Yiallourou, Sophia Kyritsi 
Publisher
Springer-Verlag 
Publication Date
Jun, 2009 
ISBN
0387789065 or 9780387789064
HARDCOVER 
793 Pages
出版済み 3週間でお届けいたします。
The delivery time takes 3 weeks

¥ 30,468 (tax included)

Description

Accurate models to describe real-world phenomena are indispensable for research in such scientific fields as physics, engineering, biology, chemistry, and economics. The tools and techniques of applied analysis facilitate the development of mathematical models and can thereby serve as an excellent resource for students and researchers in various scientific and mathematical disciplines. This self-contained, comprehensive handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis. Unique features of the Handbook of Applied Analysis: . Presents an accessible introduction to modern analysis, while still serving as a useful reference for researchers and practitioners; . Covers a large number of diverse topics: smooth and nonsmooth differential calculus, optimal control, fixed point theory, critical point theory, linear and nonlinear eigenvalue problems, nonlinear boundary value problems, set-valued analysis, game theory, stochastic analysis, and evolutionary equations; . Serves as a complete guide to the theory of nonlinear analysis; . Includes numerous examples that demonstrate and expand upon the topics presented; . Suggests many directions for further research and study. In this one volume, the reader can find many of the most important theoretical trends in nonlinear analysis and applications to different fields. These features, together with an extensive bibliography, make the volume a valuable tool for every researcher working on nonlinear analysis.

Contents

Series Preface . ix
Preface xi
1 Smooth and Nonsmooth Calculus 1
1.1 Gateaux and Frechet Derivatives 2
1.2 Convex Functions . 12
1.3 Locally Lipschitz Functions . 27
1.4 Variational Geometry 35
1.5 Γ-Convergence 45
1.6 Remarks . 60
2 Extremal Problems and Optimal Control 63
2.1 Lower Semicontinuity 64
2.2 Constrained Minimization Problems . 72
2.3 Saddle Points and Duality 79
2.4 Variational Principles 89
2.5 Calculus of Variations 98
2.6 Optimal Control 111
2.7 Remarks . 144
3 Nonlinear Operators and Fixed Points . 147
3.1 Compact and Fredholm Operators . 148
3.2 Monotone and Accretive Operators 162
3.3 Degree Theory 196
3.4 Metric Fixed Points 224
3.5 Topological Fixed Points . 237
3.6 Order and Fixed Points 245
3.7 Remarks . 263
4 Critical Point Theory and Variational Methods 267
4.1 Critical Point Theory 268
4.2 Ljusternik Schnirelmann Theory 289
4.3 Spectrum of the Laplacian and of the p-Laplacian . 297
4.4 Abstract Eigenvalue Problems. 334
4.5 Bifurcation Theory 340
4.6 Remarks . 349
5 Boundary Value Problems Hamiltonian Systems 351
5.1 Variational Method 352
5.2 Method of Upper Lower Solutions . 380
5.3 Degree-Theoretic Methods 404
5.4 Nonlinear Eigenvalue Problems 421
5.5 Maximum and Comparison Principles 432
5.6 Periodic Solutions for Hamiltonian Systems . 440
5.7 Remarks . 450
6 Multivalued Analysis 455
6.1 Continuity of Multifunctions 456
6.2 Measurability of Multifunctions . 470
6.3 Continuous and Measurable Selectors 475
6.4 Decomposable Sets and Set-Valued Integration 487
6.5 Fixed Points and Caratheodory Multifunctions 504
6.6 Convergence of Sets 514
6.7 Remarks . 524
7 Economic Equilibrium and Optimal Economic Planning . 529
7.1 Perfectly Competitive Economies: Core and Walras Equilibria 530
7.2 Infinite Horizon Multisector Growth Models 542
7.3 Turnpike Theorems 558
7.4 Stochastic Growth Models 567
7.5 Continuous-Time Growth Models 589
7.6 Expected Utility Hypothesis 599
7.7 Remarks . 606
8 Game Theory 609
8.1 Noncooperative Games Nash Equilibrium 610
8.2 Cooperative Games 617
8.3 Cournot Nash Equilibria for Random Games . 624
8.4 Bayesian Games . 628
8.5 Stochastic Games. . 632
8.6 Approximate Equilibria 644
8.7 Remarks . 649
9 Uncertainty, Information, Decision Making 651
9.1 Mathematical Space of Information 652
9.2 The ex-Post View . 662
9.3 The ex-ante View . 668
9.4 Convergence of σ-Fields and Prediction Sequences . 673
9.5 Games with Incomplete Information . 680
9.6 Markov Decision Chains with Unbounded Costs . 684
9.7 Remarks . 689
10 Evolution Equations . 691
10.1 Lebesgue Bochner Spaces 692
10.2 Semilinear Evolution Equations . 701
10.3 Nonlinear Evolution Equations 718
10.4 Second-Order Nonlinear Evolution Equations . 740
10.5 Remarks . 750
References . 753
List of Symbols 781
Index 783

送料無料にてお届け

ご注文商品は海外からのお取り寄せのため,納期は3~5週間程頂きます。入荷の遅延,出版延期など納期に遅れが見込まれる場合はメールにてお知らせ致します

公費/校費/社費でのお支払い

ご注文の際,お支払方法を選択して頂く画面が表示されますので,「公費/校費/社費」をお選び頂き必要書類をご指定下さい。公費/校費/社費の場合でも、HP掲載価格で承ります。

書籍が見つからない場合

お問い合わせメールより書籍のタイトルや ISBNなど、お手持ちの情報をお知らせ下さい。お見積り、ご注文を承ります。

SSL グローバルサインのサイトシール