Theory Of Differential Equations With Unbounded Delay
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Theory Of Differential Equations With Unbounded Delay
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Author : V. Lakshmikantham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Theory Of Differential Equations With Unbounded Delay written by V. Lakshmikantham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the subtle differences of the various equations with delays. Furthermore, such a unified theory would avoid duplication and expose open questions that are significant for future research. It is in this spirit that the authors view the importance of their monograph, which presents a systematic and unified theory of recent developments of equations with unbounded delay, describes the current state of the theory showing the essential unity achieved, and provides a general structure applicable to a variety of problems. It is the first book that: (i) presents a unified framework to investigate the basic existence theory for a variety of equations with delay; (ii) treats the classification of equations with memory precisely so as to bring out the subtle differences between them; (iii) develops a systematic study of stability theory in terms of two different measures which includes several known concepts; and (iv) exhibits the advantages of employing Lyapunov functions on product spaces as well as the method of perturbing Lyapunov functions. This book will be of value to researchers and advanced graduate students in mathematics, electrical engineering and biomathematics.
Functional Differential Equations With Infinite Delay
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Author : Yoshiyuki Hino
language : en
Publisher: Springer
Release Date : 2006-11-14
Functional Differential Equations With Infinite Delay written by Yoshiyuki Hino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
In the theory of functional differential equations with infinite delay, there are several ways to choose the space of initial functions (phase space); and diverse (duplicated) theories arise, according to the choice of phase space. To unify the theories, an axiomatic approach has been taken since the 1960's. This book is intended as a guide for the axiomatic approach to the theory of equations with infinite delay and a culmination of the results obtained in this way. It can also be used as a textbook for a graduate course. The prerequisite knowledge is foundations of analysis including linear algebra and functional analysis. It is hoped that the book will prepare students for further study of this area, and that will serve as a ready reference to the researchers in applied analysis and engineering sciences.
Equations With Unbounded Delay
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Author : C. Corduneanu
language : en
Publisher:
Release Date : 1979
Equations With Unbounded Delay written by C. Corduneanu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Delay differential equations categories.
Delay Differential Equations And Applications
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Author : O. Arino
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-07
Delay Differential Equations And Applications written by O. Arino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-07 with Mathematics categories.
This book groups material that was used for the Marrakech 2002 School on Delay Di?erential Equations and Applications. The school was held from September 9-21 2002 at the Semlalia College of Sciences of the Cadi Ayyad University, Marrakech, Morocco. 47 participants and 15 instructors originating from 21 countries attended the school. Fin- cial limitations only allowed support for part of the people from Africa andAsiawhohadexpressedtheirinterestintheschoolandhadhopedto come. Theschoolwassupportedby?nancementsfromNATO-ASI(Nato advanced School), the International Centre of Pure and Applied Mat- matics (CIMPA, Nice, France) and Cadi Ayyad University. The activity of the school consisted in courses, plenary lectures (3) and communi- tions (9), from Monday through Friday, 8. 30 am to 6. 30 pm. Courses were divided into units of 45mn duration, taught by block of two units, with a short 5mn break between two units within a block, and a 25mn break between two blocks. The school was intended for mathematicians willing to acquire some familiarity with delay di?erential equations or enhance their knowledge on this subject. The aim was indeed to extend the basic set of knowledge, including ordinary di?erential equations and semilinearevolutionequations, suchasforexamplethedi?usion-reaction equations arising in morphogenesis or the Belouzov-Zhabotinsky ch- ical reaction, and the classic approach for the resolution of these eq- tions by perturbation, to equations having in addition terms involving past values of the solution.
Basic Theory Of Fractional Differential Equations Third Edition
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Author : Yong Zhou
language : en
Publisher: World Scientific
Release Date : 2023-10-06
Basic Theory Of Fractional Differential Equations Third Edition written by Yong Zhou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Mathematics categories.
This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.
Advanced Functional Evolution Equations And Inclusions
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Author : Saïd Abbas
language : en
Publisher: Springer
Release Date : 2015-06-30
Advanced Functional Evolution Equations And Inclusions written by Saïd Abbas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-30 with Mathematics categories.
This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.
Theory And Applications Of Partial Functional Differential Equations
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Author : Jianhong Wu
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-09-26
Theory And Applications Of Partial Functional Differential Equations written by Jianhong Wu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-26 with Mathematics categories.
Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.
Discrete Dynamics And Difference Equations Proceedings Of The Twelfth International Conference On Difference Equations And Applications
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Author : Saber N Elaydi
language : en
Publisher: World Scientific
Release Date : 2010-11-02
Discrete Dynamics And Difference Equations Proceedings Of The Twelfth International Conference On Difference Equations And Applications written by Saber N Elaydi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-02 with Mathematics categories.
This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal.The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.
Lyapunov Functionals And Stability Of Stochastic Functional Differential Equations
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Author : Leonid Shaikhet
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-29
Lyapunov Functionals And Stability Of Stochastic Functional Differential Equations written by Leonid Shaikhet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-29 with Technology & Engineering categories.
Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: • inverted controlled pendulum; • Nicholson's blowflies equation; • predator-prey relationships; • epidemic development; and • mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.
Stability Of Differential Equations With Aftereffect
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Author : N.V. Azbelev
language : en
Publisher: CRC Press
Release Date : 2002-10-03
Stability Of Differential Equations With Aftereffect written by N.V. Azbelev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-03 with Mathematics categories.
Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics. The authors provide background material on the modern theory of functional differential equations and introduce some new flexible methods for investigating the asymptotic behaviour of solutions to a range of equations. The treatment also includes some results from the authors' research group based at Perm and provides a useful reference text for graduates and researchers working in mathematical and engineering science.