Nonlinear Problems in Abstract Cones

Preface

Chapter 1. Basic Properties of Cones


1.0 Introduction


1.1 Notarial Cones


1.2 Regular and Fully Regular Cones


1.3 Minlhedral and Strongly Minlhedral Cones


1.4 Positive Linear Functional


1.5 The e-Norm and Hilbert's Protective Metric


1.6 Notes and Comments

Chapter 2. Positive Fixed Point Theory


2.0 Introduction


2.1 Fixed Points of Monotone Operators


2.2 Fixed Points of Concave and Convex Operators


2.3 Fixed Points ο£ Cone Expansion and Compression


2.4 Multiple Fixed Point Theorems


2.5 Fixed Points of Domain Expansion and Compression


2.6 Notes and Comments

Chapter 3. Applications to Nonlinear Integal Equations


3.0 Introduction


3.1 integral Equations of Polynomial Type


3.2 Eigenvalues and Elgenfunctions


3.3 Some Nonlinear Integral Equations Arising in Science


3.4 Infinitely Many Solutions Obtained by Variational Methods


3.5 Notes and Comments

Chapter 4. Applications to Nonlinear Differential Equations


4.0 Introduction


4.1 Differential Inequalities


4.2 Flow-Invariant Sets


4.3 Method of Upper and Lower Solutions


4.4 Monotone Iterative Technique


4.5 Method of Upper and Lower Quasi-Solutions


4.6 Cone-Valued Lyapunov Functions and Stabltity Theory


4.7 Notes and Comments

Appendix

A.1 Separation Theorems of Convex Sets

A.2 Zorn's Lemma

A.3 Leray-Schauder Degree

A.4 Properties of Nemitskii Operators

A.5 Extension Theorems

References