Said R. Grace's Books

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

By: R.P. Agarwal,Said R. Grace,Donal O'Regan

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

By: R.P. Agarwal,Said R. Grace,Donal O'Regan

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.

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Page Count

685

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401725152

ISBN 13

9789401725156

Oscillation Theory for Second Order Dynamic Equations

By: Ravi P. Agarwal,Said R. Grace,Donal O'Regan

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Oscillation Theory for Second Order Dynamic Equations

By: Ravi P. Agarwal,Said R. Grace,Donal O'Regan

The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journa

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Page Count

416

Publisher

CRC Press

Published Date

ISBN 10

020322289X

ISBN 13

9780203222898

Oscillation Theory for Difference and Functional Differential Equations

By: R.P. Agarwal,Said R. Grace,Donal O'Regan

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Oscillation Theory for Difference and Functional Differential Equations

By: R.P. Agarwal,Said R. Grace,Donal O'Regan

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.

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Page Count

344

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401594015

ISBN 13

9789401594011

Book's by Said R. Grace

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

Oscillation Theory for Second Order Dynamic Equations

Oscillation Theory for Second Order Dynamic Equations

Oscillation Theory for Difference and Functional Differential Equations

Oscillation Theory for Difference and Functional Differential Equations

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