Topological Methods for Differential Equations and Inclusions - Graef, John R.; Henderson, Johnny; Ouahab, Abdelghani; Taylor and Francis (Boca Raton, FL : CRC Press, 2018)
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.
Introduction -- 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 -- 10 Semigroups -- 11 Systems of Impulsive Differential Equations on the Half-line -- 12 Differential Inclusions -- 13 Random Systems of Differential Equations -- 14 Random Fractional Differential 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 -- 19 Appendix.
Includes bibliographical references and index.
Also available in print format.
Keywords: Differential equations; Topology; Differential inclusions; MATHEMATICS / Differential Equations; MATHEMATICS / Geometry / General; Fixed Point Theorems; Generalized metric space; Impulsive Differential Equations; Measurable Multifunctions; Multi-valued Analysis; Electronic books