Nonoscillation Theory of Functional Differential Equations with Applications

Nonoscillation Theory of Functional Differential Equations with Applications

Author: Ravi P. Agarwal

Publisher: Springer Science & Business Media

Published: 2012-04-23

Total Pages: 526

ISBN-13: 1461434556

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This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.​


Nonoscillation and Oscillation Theory for Functional Differential Equations

Nonoscillation and Oscillation Theory for Functional Differential Equations

Author: Ravi P. Agarwal

Publisher: CRC Press

Published: 2004-08-30

Total Pages: 400

ISBN-13: 0203025741

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This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential eq


Oscillation Theory for Functional Differential Equations

Oscillation Theory for Functional Differential Equations

Author: Lynn Erbe

Publisher: Routledge

Published: 2017-10-02

Total Pages: 504

ISBN-13: 135142632X

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Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.


Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

Author: R.P. Agarwal

Publisher: Springer Science & Business Media

Published: 2002-07-31

Total Pages: 700

ISBN-13: 9781402008023

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In this monograph, the authors present a compact, thorough, systematic, and self-contained oscillation theory for linear, half-linear, superlinear, and sublinear second-order ordinary differential equations. An important feature of this monograph is the illustration of several results with examples of current interest. This book will stimulate further research into oscillation theory. This book is written at a graduate level, and is intended for university libraries, graduate students, and researchers working in the field of ordinary differential equations.


Half-Linear Differential Equations

Half-Linear Differential Equations

Author: Ondrej Dosly

Publisher: Elsevier

Published: 2005-07-06

Total Pages: 533

ISBN-13: 0080461239

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The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.- The first complete treatment of the qualitative theory of half-linear differential equations.- Comparison of linear and half-linear theory.- Systematic approach to half-linear oscillation and asymptotic theory.- Comprehensive bibliography and index.- Useful as a reference book in the topic.


Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations

Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations

Author: Leonid Berezansky

Publisher: CRC Press

Published: 2020-05-18

Total Pages: 605

ISBN-13: 1000048632

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Asymptotic properties of solutions such as stability/ instability,oscillation/ nonoscillation, existence of solutions with specific asymptotics, maximum principles present a classical part in the theory of higher order functional differential equations. The use of these equations in applications is one of the main reasons for the developments in this field. The control in the mechanical processes leads to mathematical models with second order delay differential equations. Stability and stabilization of second order delay equations are one of the main goals of this book. The book is based on the authors’ results in the last decade. Features: Stability, oscillatory and asymptotic properties of solutions are studied in correlation with each other. The first systematic description of stability methods based on the Bohl-Perron theorem. Simple and explicit exponential stability tests. In this book, various types of functional differential equations are considered: second and higher orders delay differential equations with measurable coefficients and delays, integro-differential equations, neutral equations, and operator equations. Oscillation/nonoscillation, existence of unbounded solutions, instability, special asymptotic behavior, positivity, exponential stability and stabilization of functional differential equations are studied. New methods for the study of exponential stability are proposed. Noted among them inlcude the W-transform (right regularization), a priory estimation of solutions, maximum principles, differential and integral inequalities, matrix inequality method, and reduction to a system of equations. The book can be used by applied mathematicians and as a basis for a course on stability of functional differential equations for graduate students.


Oscillation Theory Of Partial Differential Equations

Oscillation Theory Of Partial Differential Equations

Author: Norio Yoshida

Publisher: World Scientific Publishing Company

Published: 2008-10-13

Total Pages: 339

ISBN-13: 9813107375

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This unique book is designed to provide the reader with an exposition of interesting aspects — encompassing both rudimentary and advanced knowledge — of oscillation theory of partial differential equations, which dates back to the publication in 1955 of a paper by Ph Hartman and A Wintner. The objective of oscillation theory is to acquire as much information as possible about the qualitative properties of solutions of differential equations through the analysis of laws governing the distribution of zeros of solutions as well as the asymptotic behavior of solutions of differential equations under consideration.This textbook on oscillation theory of partial differential equations is useful for both specialists and graduate students working in the field of differential equations. The book will also help to stimulate further progress in the study of oscillation theory and related subjects.


Oscillation Theory for Difference and Functional Differential Equations

Oscillation Theory for Difference and Functional Differential Equations

Author: R.P. Agarwal

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 344

ISBN-13: 9401594015

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This monograph is devoted to a rapidly developing area of research of the qualitative theory of difference and functional differential equations. In fact, in the last 25 years Oscillation Theory of difference and functional differential equations has attracted many researchers. This has resulted in hundreds of research papers in every major mathematical journal, and several books. In the first chapter of this monograph, we address oscillation of solutions to difference equations of various types. Here we also offer several new fundamental concepts such as oscillation around a point, oscillation around a sequence, regular oscillation, periodic oscillation, point-wise oscillation of several orthogonal polynomials, global oscillation of sequences of real valued functions, oscillation in ordered sets, (!, R, ~)-oscillate, oscillation in linear spaces, oscillation in Archimedean spaces, and oscillation across a family. These concepts are explained through examples and supported by interesting results. In the second chapter we present recent results pertaining to the oscil lation of n-th order functional differential equations with deviating argu ments, and functional differential equations of neutral type. We mainly deal with integral criteria for oscillation. While several results of this chapter were originally formulated for more complicated and/or more general differ ential equations, we discuss here a simplified version to elucidate the main ideas of the oscillation theory of functional differential equations. Further, from a large number of theorems presented in this chapter we have selected the proofs of only those results which we thought would best illustrate the various strategies and ideas involved.


Difference Equations and Inequalities

Difference Equations and Inequalities

Author: Ravi P. Agarwal

Publisher: CRC Press

Published: 2000-01-27

Total Pages: 1010

ISBN-13: 9781420027020

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A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and


Oscillation Theory for Functional Differential Equations

Oscillation Theory for Functional Differential Equations

Author: Lynn Erbe

Publisher: Routledge

Published: 2017-10-02

Total Pages: 500

ISBN-13: 1351426311

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Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.