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.

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.

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

Differential/Difference Equations
Differential/Difference Equations

Author: Ioannis Dassios

Publisher: Mdpi AG

Published: 2021-11-30

Total Pages: 286

ISBN-13: 9783036523873

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The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations.

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 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.

An Introduction to Difference Equations
An Introduction to Difference Equations

Author: Saber N. Elaydi

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 398

ISBN-13: 1475791682

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This book grew out of lecture notes I used in a course on difference equations that I taught at Trinity University for the past five years. The classes were largely pop ulated by juniors and seniors majoring in Mathematics, Engineering, Chemistry, Computer Science, and Physics. This book is intended to be used as a textbook for a course on difference equations at the level of both advanced undergraduate and beginning graduate. It may also be used as a supplement for engineering courses on discrete systems and control theory. The main prerequisites for most of the material in this book are calculus and linear algebra. However, some topics in later chapters may require some rudiments of advanced calculus. Since many of the chapters in the book are independent, the instructor has great flexibility in choosing topics for the first one-semester course. A diagram showing the interdependence of the chapters in the book appears following the preface. This book presents the current state of affairs in many areas such as stability, Z-transform, asymptoticity, oscillations and control theory. However, this book is by no means encyclopedic and does not contain many important topics, such as Numerical Analysis, Combinatorics, Special functions and orthogonal polyno mials, boundary value problems, partial difference equations, chaos theory, and fractals. The nonselection of these topics is dictated not only by the limitations imposed by the elementary nature of this book, but also by the research interest (or lack thereof) of the author.