Contents
Part A
1 Elliptic Equations
1.1 Introduction
1.2 Monotone Iterates: A Preview
1.3 Monotone Iterative Technique
1.4 Generalized Quasilinearization
1.5 Weakly Coupled Mixed Monotone Systems
1.6 Elliptic Systems in Unbounded Domains
1.7 Monotone Iterative Technique (MIT) for Systems in Unbounded Domains
1.8 Notes and Comments
2 Parabolic Equations
2.1 Introduction
2.2 Comparison Theorem
2.3 Monotone Iterative Technique
2.4 Generalized Quasilinearization
2.5 Monotone Flows and Mixed Monotone Systems
2.7 Stability and Vector Lyapunov Functions
2.8 Notes and Comments
3 Impulsive Parabolic Equations
3.1 Introduction
3.2 Comparison Results for Impulsive Parabolic Systems (IPSs)
3.3 Coupled Lower and Upper Solutions
3.4 Generalized Quasilinearization
3.5 Population Dynamics with Impulses
3.6 Notes and Comments
4 Hyperbolic Equations
4.1 Introduction
4.2 Variation of Parameters (VP) and Comparison Results
4.3 Monotone Iterative Technique
4.4 The Method of Generalized Quasilinearization
4.5 Notes and Comments
Part B
5 Elliptic Equations
5.1 Introduction
5.2 Comparison Result
5.3 Monotone Iterative Technique (MIT): Semilinear Problems
5.4 Monotone Iterative Technique (MIT): Quasilinear Problems
5.5 Monotone Iterative Technique (MIT): Degenerate Problems
5,6 Generalized Quasilinearization (GQ): Semilinear Problems
5.7 Generalized Quasilinearization (GQ): quasilinear Problems
7.8 Generalized Quasilinearization (GQ): Degenerate Problems
7.9 Notes and Comments
6 Parabolic Equations
6.1 Introduction
6.2 Monotone Iterative Technique
6.3 Generalized Quasilinearization
6.4 Nonlocal Problems: Existence and Comparison Results
6.5 Generalized Quasilinearization (GQ): Nonlocal Problems
6.6 Quasilinear Problems: Existence and Comparison Results
6.7 Generalized Quasilinearization (GQ): Quasilinear Problems
6.8 Notes and Comments
7 Hyperbolic Equations
7.1 Introduction
7.2 Notation and Comparison Results
7.3 Monotone Iterative Technique
7.4 Generalized Quasilinearization
7.5 Notes and Comments
Appendix A