Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.
Table of Contents
1 Background in Multi-valued Analysis
2 Hausdorff□-Pompeiu Metric Topology
3 Measurable Multifunctions
4 Continuous Selection Theorems
5 Linear Multivalued Operators
6 Fixed Point Theorems
7 Generalized Metric and Banach Spaces
8 Fixed Point Theorems in Vector Metric and Banach Spaces
9 Random □fixed point theorem
11 Systems of Impulsive Diff□erential Equations on the Half-line
12 Diff□erential Inclusions
13 Random Systems of Diff□erential Equations
14 Random Fractional Di□fferential Equations via Hadamard Fractional Derivative
15 Existence Theory for Systems of Discrete Equations
16 Discrete Inclusions
17 Semilinear System of Discrete Equations
18 Discrete Boundary Value Problems
John R. Graef is professor of mathematics at the University of Tennessee at Chattanooga and previously was on the faculty at Mississippi State University.
Johnny Henderson is distinguished professor of mathematics at Baylor University. He also has held faculty positions at Auburn University and the Missouri University of Science and Technology. He is an Inaugural Fellow of the American Mathematical Society.
Abdelghani Ouahab is professor of Mathematics, Laboratory of Mathematics, Djilali-Liab\'es University Sidi Bel Abb\'es , Algeria
Each of the authors of this book has extensive research interests, including: boundary value problems for ordinary and functional differential equations and inclusions; difference equations; impulsive systems; fractional equations; dynamic equations on time scales; integral equations; boundary value problems; nonlinear oscillations, and applications to biological systems; functional differential equations and dynamic equations on time scales, along with extensions and generalizations involving multivalued analysis, and as well as in fractional analogues of those topics.