Download or read book Oscillations Of Third Order Nonlinear Neutral Differential Equations written by Mohammed Bushra and published by LAP Lambert Academic Publishing. This book was released on 2015-07-15 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of functional differential equations in recent years has attracted the attention of many researchers, in the theory and its applications. The simplest and perhaps most natural type of functional differential equation is a "delay differential equation" .This means an equation expressing some derivative of x at time t in terms of x, the values of the function x at previous times .The importance of the delay differential equations comes from its huge applications for instance, the study of problems connected with combustion in rocket motion, the problem of planning in economics, biological problems, population dynamics, the logistic equation, and population growth and mechanics, nuclear reactors, heat flow, neural networks, microbiology, ecology, and physiology, as well as many other applications .The study of oscillation and asymptotic properties of solutions of neutral differential equations with positive and negative coefficients has attracted a good bit of attention in the last several years .
Download or read book Oscillation Theory for Functional Differential Equations written by Lynn Erbe and published by Routledge. This book was released on 2017-10-02 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Oscillation Theory for Neutral Differential Equations with Delay written by D.D Bainov and published by CRC Press. This book was released on 1991-01-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: With neutral differential equations, any lack of smoothness in initial conditions is not damped and so they have proven to be difficult to solve. Until now, there has been little information to help with this problem. Oscillation Theory for Neutral Differential Equations with Delay fills a vacuum in qualitative theory of functional differential equations of neutral type. With much of the presented material previously unavailable outside Eastern Europe, this authoritative book provides a stimulus to research the oscillatory and asymptotic properties of these equations. It examines equations of first, second, and higher orders as well as the asymptotic behavior for tending toward infinity. These results are then generalized for partial differential equations of neutral type. The book also describes the historical development of the field and discusses applications in mathematical models of processes and phenomena in physics, electrical control and engineering, physical chemistry, and mathematical biology. This book is an important tool not only for mathematicians, but also for specialists in many fields including physicists, engineers, and biologists. It may be used as a graduate-level textbook or as a reference book for a wide range of subjects, from radiophysics to electrical and control engineering to biological science.
Download or read book Oscillation of Solutions of Third Order Nonlinear Differential Equations written by Wayne M. Wanamaker and published by . This book was released on 1971 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Nonlinear Oscillations written by Ronald E. Mickens and published by CUP Archive. This book was released on 1981 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory account of the equations describing nonlinear oscillations & the methods for solving them.
Download or read book Nonoscillation and Oscillation Theory for Functional Differential Equations written by Ravi P. Agarwal and published by CRC Press. This book was released on 2004-08-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 equations, second-order delay and ordinary differential equations, higher-order delay differential equations, and systems of nonlinear differential equations. The final chapter explores key aspects of the oscillation of dynamic equations on time scales-a new and innovative theory that accomodates differential and difference equations simultaneously.
Download or read book Nonlinear Differential Equations and Dynamical Systems written by Feliz Manuel Minhós and published by MDPI. This book was released on 2021-04-15 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Download or read book Discrete Oscillation Theory written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2005 with total page 977 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as very recent results in that area. While there are several books on difference equations and also on oscillation theory for ordinary differential equations, there is until now no book devoted solely to oscillation theory for difference equations. This book is filling the gap, and it can easily be used as an encyclopedia and reference tool for discrete oscillation theory. In nine chapters, the book covers a wide range of subjects, including oscillation theory for second-order linear difference equations, systems of difference equations, half-linear difference equations, nonlinear difference equations, neutral difference equations, delay difference equations, and differential equations with piecewise constant arguments. This book summarizes almost 300 recent research papers and hence covers all aspects of discrete oscillation theory that have been discussed in recent journal articles. The presented theory is illustrated with 121 examples throughout the book. Each chapter concludes with a section that is devoted to notes and bibliographical and historical remarks. The book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. Besides serving as a reference tool for researchers in difference equations, this book can also be easily used as a textbook for undergraduate or graduate classes. It is written at a level easy to understand for college students who have had courses in calculus.
Download or read book Oscillation Theory for Difference and Functional Differential Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Half Linear Differential Equations written by Ondrej Dosly and published by Elsevier. This book was released on 2005-07-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a systematic and compact treatment of the qualitative theory of half-linear differential 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.
Download or read book Oscillation Nonoscillation Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations written by Leonid Berezansky and published by CRC Press. This book was released on 2020-05-18 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Multivariate Approximation for solving ODE and PDE written by Clemente Cesarano and published by MDPI. This book was released on 2020-12-07 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents collective works published in the recent Special Issue (SI) entitled "Multivariate Approximation for Solving ODE and PDE". These papers describe the different approaches and related objectives in the field of multivariate approximation. The articles in fact present specific contents of numerical methods for the analysis of the approximation, as well as the study of ordinary differential equations (for example oscillating with delay) or that of partial differential equations of the fractional order, but all linked by the objective to present analytical or numerical techniques for the simplification of the study of problems involving relationships that are not immediately computable, thus allowing to establish a connection between different fields of mathematical analysis and numerical analysis through different points of view and investigation. The present contents, therefore, describe the multivariate approximation theory, which is today an increasingly active research area that deals with a multitude of problems in a wide field of research. This book brings together a collection of inter-/multi-disciplinary works applied to many areas of applied mathematics in a coherent manner.
Download or read book Oscillation Theory of Partial Differential Equations written by Norio Yoshida and published by World Scientific. This book was released on 2008 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Oscillation Theory of Differential Equations with Deviating Arguments written by G. S. Ladde and published by Marcel Dekker. This book was released on 1987 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Oscillation Theory for Second Order Dynamic Equations written by Ravi P. Agarwal and published by CRC Press. This book was released on 2002-11-21 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Contributions to the Theory of Nonlinear Oscillations AM 36 Volume III written by Solomon Lefschetz and published by Princeton University Press. This book was released on 2016-03-02 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III, will be forthcoming.
Download or read book Functional Dynamic Equations on Time Scales written by Svetlin G. Georgiev and published by Springer. This book was released on 2019-05-03 with total page 885 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.
