Topological Methods for Differential Equations and Inclusions

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John R. Graef (University of Tennessee, Chattanooga, USA University of Tennessee, Chattanooga, USA) Johnny Henderson

Topological Methods for Differential Equations and Inclusions

John R. Graef (University of Tennessee, Chattanooga, USA University of Tennessee, Chattanooga, USA), Johnny Henderson, Abdelghani Ouahab

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English

CRC Press
02 October 2018

Differential calculus & equations; Topology; Probability & statistics

Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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.

By: John R. Graef (University of Tennessee Chattanooga USA University of Tennessee Chattanooga USA), Johnny Henderson, Abdelghani Ouahab
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
Weight: 480g
ISBN: 9781138332294
ISBN 10: 1138332291
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Pages: 360
Publication Date: 02 October 2018
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Hardback
Publisher's Status: Active

Introduction. 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.

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.