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Topological Methods for Differential Equations and Inclusions / by John R. Graef, Johnny Henderson and Abdelghani Ouahab.

By: Graef, John R [author.]Contributor(s): Henderson, Johnny [author.] | Ouahab, Abdelghani [author.] | Taylor and FrancisMaterial type: TextTextLanguage: English Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics: Publisher: Boca Raton, FL : CRC Press, [2018]Copyright date: ©2019Edition: First editionDescription: 1 online resource (374 pages) : 1 illustrations, text file, PDFContent type: text Media type: computer Carrier type: online resourceISBN: 9780429446740Subject(s): Differential equations | Topology | Differential inclusions | MATHEMATICS / Differential Equations | MATHEMATICS / Geometry / General | Fixed Point Theorems | Generalized metric space | Impulsive Differential Equations | Measurable Multifunctions | Multi-valued AnalysisGenre/Form: Electronic books.Additional physical formats: Print version: : No titleDDC classification: 515/.35 LOC classification: QA372Online resources: Click here to view. Also available in print format.
Contents:
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.
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.
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Includes bibliographical references and index.

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.

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.

Also available in print format.

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