Preface to Part II/B
GENERALIZATION TO NONLINEAR STATIONARY PROBLEMS
Basic Ideas of the Theory of Monotone Operators
CHAPTER 25 Lipschitz Continuous, Strongly Monotone Operators, the Projection-lteration Method, and Monotone Potential Operators
25.1.Sequences of k-Contractive Operators
25.2.The Projection Iteration Method for k-Contractive Operators
25.3.Monotone Operators
25.4.The Main Theorem on Strongly Monotone Operators, and the Projection-Iteration Method
25.5.Monotone and Pseudomonotone Operators, and the Calculus of Variations
25.6.The Main Theorem on Monotone Potential Operators
25.7.The Main Theorem on Pseudomonotone Potential Operators
25.8.Application to the Main Theorem on Quadratic Variational Inequalities
25.9.Application to Nonlinear Stationary Conservation Laws
25.10.Projection Iteration Method for Conservation Laws
25.11.The Main Theorem on Nonlinear Stationary Conservation Laws
25.12.Duality Theory for Conservation Laws and Two-sided a posterior.i Error Estimates for the Ritz Method
25.13.The Kacanov Method for Stationary Conservation Laws
25.14.The Abstract Kacanov Method for Variational Inequalities
CHAPTER 26 Monotone Operators and Quasi-Linear Elliptic Differential Equations
26.1.Hemicontinuity and Demicontinuity
26.2.The Main Theorem on Monotone Operators
26.3.The Nemyckii Operator
26.4.Generalized Gradient Method for the Solution of the Galerkin Equations
26.5.Application to Quasi-Linear Elliptic Differential Equations of Order 2m
26.6.Proper Monotone Operators and Proper Quasi-Linear Elliptic Differential Operators
CHAPTER 27 Pseudomonotone Operators and Quasi-Linear Elliptic Differential Equations
27.1.The Conditions (M) and (S), and the Convergence of the Galerkin Method
27.2.Pseudomonotone Operators
27.3.The Main Theorem on Pseudomonotone Operators
27.4.Application to Quasi-Linear Elliptic Differential Equations
27.5.Relations Between Important Properties of Nonlinear Operators
27.6.Dual Pairs of B-Spaces
27.7.The Main Theorem on Locally Coercive Operators
27.8.Application to Strongly Nonlinear Differential Equations
CHAPTER 28 Monotone Operators and Hammerstein Integral Equations
28.1.A Factorization Theorem for Angle-Bounded Operators
28.2.Abstract Hammerstein Equations with Angle-Bounded Kernel Operators
28.3.Abstract Hammerstein Equations with Compact Kernel Operators
28.4.Application to Hammerstein Integral Equations
28.5.Application to Semilinear Elliptic Differential Equations
CHAPTER 29 Noncoercive Equations, Nonlinear Fredholm Alternatives,Locally Monotone Operators, Stability, and Bifurcation
29.1.Pseudoresolvent, Equivalent Coincidence Problems, and the Coincidence Degree
29.2.Fredholm Alternatives for Asymptotically Linear, Compact Perturbations of the Identity
29.3.Application to Nonlinear Systems of Real Equations
29.4.Application to Integral Equations
29.5.Application to Differential Equations
29.6.The Generalized Antipodal Theorem
29.7.Fredholm Alternatives for Asymptotically Linear (S)-Operators
29.8.Weak Asymptotes and Fredholm Alternatives
……
GENERALIZATION TO NONLINEAR NONSTATIONARY PROBLEMS
GENERAL THEORY OF DISCRETIZATION METHODS
Appendix
References
List of Symbols
List of Theorems
List of the Most Important Definitions
List of Schematic Overviews
List of Important Principles
Index
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