Description
Book SynopsisTopological 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 ContentsIntroduction. 1 Background in Multi-valued Analysis. 2 Hausdor□-Pompeiu Metric Topology. 3 Measurable Multifunctions. Measurable selection. 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 □xed point theorem. 10 Semigroups. 11 Systems of Impulsive Di□erential Equations on the Half-line. 12 Di□erential Inclusions. 13 Random Systems of Di□erential Equations. 14 Random Fractional Di□erential Equations via Hadamard Fractional Derivatives. 15 Existence Theory for Systems of Discrete Equations. 16 Discrete Inclusions. 17 Semilinear System of Discrete Equations. 18 Discrete Boundary Value Problems. 19 Appendix.
