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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