Qualitative Theory Of Volterra Difference Equations

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Qualitative Theory Of Volterra Difference Equations

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Author : Youssef N. Raffoul
language : en
Publisher: Springer
Release Date : 2018-09-12

Qualitative Theory Of Volterra Difference Equations written by Youssef N. Raffoul and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-12 with Mathematics categories.

This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. Applications to real-world problems and open-ended problems are included throughout. This book will be of use as a primary reference to researchers and graduate students who are interested in the study of boundedness of solutions, the stability of the zero solution, or in the existence of periodic solutions using Lyapunov functionals and the notion of fixed point theory.

Advanced Differential Equations

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Author : Youssef N. Raffoul
language : en
Publisher: Academic Press
Release Date : 2022-04-13

Advanced Differential Equations written by Youssef N. Raffoul and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-13 with Mathematics categories.

Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations. Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations. Includes content from a class-tested over multiple years with advanced undergraduate and graduate courses Presents difficult material in an accessible manner by utilizing easier, friendlier notations, multiple examples and thoughtful exercises of increasing difficulty Provides content that is appropriate for advanced classes up to, and including, a two-semester graduate course in exploring the theory and applications of ordinary differential equations Requires minimal background in real analysis and differential equations Offers a partial solutions manual for student study

Theory Of Integro Differential Equations

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Author : V. Lakshmikantham
language : en
Publisher: CRC Press
Release Date : 1995-03-15

Theory Of Integro Differential Equations written by V. Lakshmikantham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-15 with Mathematics categories.

This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract spaces. Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike.

Qualitative Theory Of Differential Equations In The Plane And In The Space With Emphasis On The Center Focus Problem And On The Lotka Volterra Systems

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Author : Valentí Ramírez Sadovski
language : en
Publisher:
Release Date : 2019

Qualitative Theory Of Differential Equations In The Plane And In The Space With Emphasis On The Center Focus Problem And On The Lotka Volterra Systems written by Valentí Ramírez Sadovski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

International Conference On Differential Equations

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Author : H.A. Antosiewicz
language : en
Publisher: Academic Press
Release Date : 2014-05-10

International Conference On Differential Equations written by H.A. Antosiewicz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

International Conference on Differential Equations contains the proceedings of an International Conference on Differential Equations held at the University of Southern California, on September 3-7, 1974. The papers review advances in the qualitative-analytic theory of differential equations and highlight three broad areas: analytic theory (singular perturbations), qualitative theory (boundary value problems), and mathematical control theory (variational methods). Comprised of 82 chapters, this book begins with a discussion on continuous extensions, their construction, and their application in the theory of differential equations. The reader is then introduced to an approach to boundary control of partial differential equations based on the theory of semigroups of operators; lower closure and existence theorems in optimal control; and a nonlinear oscillation theorem. Subsequent chapters focus on matrices of rational functions; asymptotic integration of linear differential systems; solutions near bifurcated steady states; and geometric views in existence theory. This monograph will be of interest to students and instructors of mathematics.

Volterra Equations And Applications

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Author : C. Corduneanu
language : en
Publisher: CRC Press
Release Date : 2000-01-10

Volterra Equations And Applications written by C. Corduneanu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-10 with Mathematics categories.

This volume comprises selected papers presented at the Volterra Centennial Symposium and is dedicated to Volterra and the contribution of his work to the study of systems - an important concept in modern engineering. Vito Volterra began his study of integral equations at the end of the nineteenth century and this was a significant development in the theory of integral equations and nonlinear functional analysis. Volterra series are of interest and use in pure and applied mathematics and engineering.

Some Gronwall Type Inequalities And Applications

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Author : Sever Silvestru Dragomir
language : en
Publisher:
Release Date : 2018

Some Gronwall Type Inequalities And Applications written by Sever Silvestru Dragomir and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

Some Gronwall type inequalities for kernels of L-type and application in qualitative theory of Volterra integral equations and for systems of differential equations are presented.

Delay And Functional Differential Equations And Their Applications

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Author : Klaus Schmitt
language : en
Publisher: Elsevier
Release Date : 2014-05-10

Delay And Functional Differential Equations And Their Applications written by Klaus Schmitt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.

Analytical And Numerical Methods For Volterra Equations

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Author : Peter Linz
language : en
Publisher: SIAM
Release Date : 1985-01-01

Analytical And Numerical Methods For Volterra Equations written by Peter Linz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.

Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.

Integral And Integrodifferential Equations

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Author : Ravi P. Agarwal
language : en
Publisher: CRC Press
Release Date : 2000-03-09

Integral And Integrodifferential Equations written by Ravi P. Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-09 with Mathematics categories.

This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.