ABSTRACT

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.

chapter 1|30 pages

Chapter 1

Background in Multi-valued Analysis

chapter 2|20 pages

Chapter 2

Hausdorff-Pompeiu Metric Topology

chapter 3|30 pages

Chapter 3

Measurable Multifunctions

chapter 4|4 pages

Chapter 4

Continuous Selection Theorems

chapter 5|10 pages

Chapter 5

Linear Multivalued Operators

chapter 6|32 pages

Chapter 6

Fixed Point Theorems

chapter 7|14 pages

Chapter 7

Generalized Metric and Banach Spaces

chapter 8|28 pages

Chapter 8

Fixed Point Theorems in Vector Metric and Banach Spaces

chapter 9|18 pages

Chapter 9

Random Fixed Point Theorems

chapter 10|4 pages

Chapter 10

Semigroups

chapter 11|12 pages

Chapter 11

Systems of Impulsive Differential Equations on Half-lines

chapter 12|38 pages

Chapter 12

Differential Inclusions

chapter 13|10 pages

Chapter 13

Random Systems of Differential Equations

chapter 14|18 pages

Chapter 14

Random Fractional Differential Equations

chapter 15|40 pages

Chapter 15

Existence Theory for Systems of Discrete Equations

chapter 16|6 pages

Chapter 16

Discrete Inclusions

chapter 17|12 pages

Chapter 17

Semilinear System of Discrete Equations

chapter 18|14 pages

Chapter 18

Discrete Boundary Value Problems