非线性泛函分析及其应用 第2B卷 非线性单调算子 英文版PDF|Epub|txt|kindle电子书版本下载

非线性泛函分析及其应用 第2B卷 非线性单调算子 英文版PDF格式电子书版下载

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GENERALIZATION TO NONLINEAR STATIONARY PROBLEMS469

Basic Ideas of the Theory of Monotone Operators471

CHAPTER 25 Lipschitz Continuous,Strongly Monotone Operators,the Projection-Iteration Method,and Monotone Potential Operators495

25.1．Sequences of k-Contractive Operators497

25.2．The Projection-Iteration Method for k-Contractive Operators499

25.3．Monotone Operators500

25.4．The Main Theorem on Strongly Monotone Operators,and the Projection-Iteration Method503

25.5．Monotone and Pseudomonotone Operators,and the Calculus of Variations506

25.6．The Main Theorem on Monotone Potential Operators516

25.7．The Main Theorem on Pseudomonotone Potential Operators518

25.8．Application to the Main Theorem on Quadratic Variational Inequalities519

25.9．Application to Nonlinear Stationary Conservation Laws521

25.10．Projection-Iteration Method for Conservation Laws527

25.11．The Main Theorem on Nonlinear Stationary Conservation Laws535

25.12．Duality Theory for Conservation Laws and Two-sided aposteriori Error Estimates for the Ritz Method537

25.13．The Ka？arov Method for Stationary Conservation Laws542

25.14．The Abstract Ka？anov Method for Variational Inequalities545

CHAPTER 26 Monotone Operators and Quasi-Linear Elliptic Differential Equations553

26.1．Hemicontinuity and Demicontinuity554

26.2．The Main Theorem on Monotone Operators556

26.3．The Nemyckii Operator561

26.4．Generalized Gradient Method for the Solution of the Galerkin Equations564

26.5．Application to Quasi-Linear Elliptic Differential Equations of Order 2m567

26.6．Proper Monotone Operators and Proper Quasi-Linear Elliptic Differential Operators576

CHAPTER 27 Pseudomonotone Operators and Quasi-Linear Elliptic Differential Equations580

27.1．The Conditions(M)and(S),and the Convergence of the Galerkin Method583

27.2．Pseudomonotone Operators585

27.3．The Main Theorem on Pseudomonotone Operators589

27.4．Application to Quasi-Linear Elliptic Differential Equations590

27.5．Relations Between Important Properties of Nonlinear Operators595

27.6．Dual Pairs of B-Spaces598

27.7．The Main Theorem on Locally Coercive Operators598

27.8．Application to Strongly Nonlinear Differential Equations604

CHAPTER 28 Monotone Operators and Hammerstein Integral Equations615

28.1．A Factorization Theorem for Angle-Bounded Operators619

28.2．Abstract Hammerstein Equations with Angle-Bounded Kernel Operators620

28.3．Abstract Hammerstein Equations with Compact Kernel Operators625

28.4．Application to Hammerstein Integral Equations627

28.5．Application to Semilinear Elliptic Differential Equations632

CHAPTER 29 Noncoercive Equations,Nonlinear Fredholm Alternatives,Locally Monotone Operators,Stability,and Bifurcation639

29.1．Pseudoresolvent,Equivalent Coincidence Problems,and the Coincidence Degree643

29.2．Fredholm Alternatives for Asymptotically Linear,Compact Perturbations of the Identity650

29.3．Application to Nonlinear Systems of Real Equations652

29.4．Application to Integral Equations653

29.5．Application to Differential Equations653

29.6．The Generalized Antipodal Theorem654

29.7．Fredholm Alternatives for Asymptotically Linear(S)-Operators657

29.8．Weak Asymptotes and Fredholm Alternatives657

29.9．Application to Semilinear Elliptic Differential Equations of the Landesman-Lazer Type661

29.10．The Main Theorem on Nonlinear Proper Fredholm Operators665

29.11．Locally Strictly Monotone Operators677

29.12．Locally Regularly Monotone Operators,Minima,and Stability679

29.13．Application to the Buckling of Beams697

29.14．Stationary Points of Functionals706

29.15．Application to the Principle of Stationary Action708

29.16．Abstract Statical Stability Theory709

29.17．The Continuation Method712

29.18．The Main Theorem of Bifurcation Theory for Fredholm Operators of Variational Type712

29.19．Application to the Calculus of Variations722

29.20．A General Bifurcation Theorem for the Euler Equations and Stability730

29.21．A Local M ultiplicity Theorem733

29.22．A Global Multiplicity Theorem735

GENERALIZATION TO NONLINEAR NONSTATIONARY PROBLEMS765

CHAPTER 30 First-Order Evolution Equations and the Galerkin Method767

30.1．Equivalent Formulations of First-Order Evolution Equations767

30.2．The Main Theorem on Monotone First-Order Evolution Equations770

30.3．Proof of the Main Theorem771

30.4．Application to Quasi-Linear Parabolic Differential Equations of Order 2m779

30.5．The Main Theorem on Semibounded Nonlinear Evolution Equations783

30.6．Application to the Generalized Korteweg-de Vries Equation790

CHAPTER 31 Maximal Accretive Operators,Nonlinear Nonexpansive Semigroups,and First-Order Evolution Equations817

31.1．The Main Theorem819

31.2．Maximal Accretive Operators820

31.3．Proof of the Main Theorem822

31.4．Application to Monotone Coercive Operators on B-Spaces827

31.5．Application to Quasi-Linear Parabolic Differential Equations829

31.6．A Look at Quasi-Linear Evolution Equations830

31.7．A Look at Quasi-Linear Parabolic Systems Regarded as Dynamical Systems832

CHAPTER 32 Maximal Monotone Mappings840

32.1 Basic Ideas843

32.2．Definition of Maximal Monotone Mappings850

32.3．Typical Examples for Maximal Monotone Mappings854

32.4．The Main Theorem on Pseudomonotone Perturbations of Maximal Monotone Mappings866

32.5．Application to Abstract Hammerstein Equations873

32.6．Application to Hammerstein Integral Equations874

32.7．Application to Elliptic Variational Inequalities874

32.8．Application to First-Order Evolution Equations876

32.9．Application to Time-Periodic Solutions for Quasi-Linear Parabolic Differential Equations877

32.10．Application to Second-Order Evolution Equations879

32.11．Regularization of Maximal Monotone Operators881

32.12．Regularization of Pseudomonotone Operators883

32.13．Local Boundedness of Monotone Mappings884

32.14．Characterization of the Surjectivity of Maximal Monotone Mappings886

32.15．The Sum Theorem888

32.16．Application to Elliptic Variational Inequalities892

32.17．Application to Evolution Variational Inequalities893

32.18．The Regularization Method for Nonuniquely Solvable Operator Equations894

32.19．Characterization of Linear Maximal Monotone Operators897

32.20．Extension of Monotone Mappings899

32.21．3-Monotone Mappings and Their Generalizations901

32.22．The Range of Sum Operators906

32.23．Application to Hammerstein Equations908

32.24．The Characterization of Nonexpansive Semigroups in H-Spaces909

CHAPTER 33 Second-Order Evolution Equations and the Galerkin Method919

33.1．The Original Problem921

33.2．Equivalent Formulations of the Original Problem921

33.3．The Existence Theorem923

33.4．Proof of the Existence Theorem924

33.5．Application to Quasi-Linear Hyperbolic Differential Equations928

33.6．Strong Monotonicity,Systems of Conservation Laws,and Quasi-Linear Symmetric Hyperbolic Systems930

33.7．Three Important General Phenomena934

33.8．The Formation of Shocks935

33.9．Blowing-Up Effects937

33.10．Blow-Up of Solutions for Semilinear Wave Equations944

33.11．A Look at Generalized Viscosity Solutions of Hamilton-Jacobi Equations947

GENERAL THEORY OF DISCRETIZATION METHODS959

CHAPTER 34 Inner Approximation Schemes,A-Proper Operators,and the Galerkin Method963

34.1．Inner Approximation Schemes963

34.2．The Main Theorem on Stable Discretization Methods with Inner Approximation Schemes965

34.3．Proof of the Main Theorem968

34.4．Inner Approximation Schemes in H-Spaces and the Main Theorem on Strongly Stable Operators969

34.5．Inner Approximation Schemes in B-Spaces972

34.6．Application to the Numerical Range of Nonlinear Operators974

CHAPTER 35 External Approximation Schemes,A-Proper Operators,and the Difference Method978

35.1．External Approximation Schemes980

35.2．Main Theorem on Stable Discretization Methods with External Approximation Schemes982

35.3．Proof of the Main Theorem984

35.4．Discrete Sobolev Spaces985

35.5．Application to Difference Methods988

35.6．Proof of Convergence990

CHAPTER 36 Mapping Degree for A-Proper Operators997

36.1．Definition of the Mapping Degree998

36.2．Properties of the Mapping Degree1000

36.3．The Antipodal Theorem for A-Proper Operators1000

36.4．A General Existence Principle1001

Appendix1009

References1119

List of Symbols1163

List of Theorems1174

List of the Most Important Definitions1179

List of Schematic Overviews1182

List of Important Principles1183

Index1189