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Oscillation Theory For Functional Differential Equations
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Book Synopsis Oscillation Theory for Functional Differential Equations by : Lynn Erbe
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 504 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.
Book Synopsis Oscillation Theory for Difference and Functional Differential Equations by : R.P. Agarwal
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.
Book Synopsis Nonoscillation Theory of Functional Differential Equations with Applications by : Ravi P. Agarwal
Download or read book Nonoscillation Theory of Functional Differential Equations with Applications written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonoscillation and Oscillation Theory for Functional Differential Equations by : Ravi P. Agarwal
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 eq
Book Synopsis Oscillation Theory for Neutral Differential Equations with Delay by : D.D Bainov
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.
Book Synopsis Oscillation Theory of Two-Term Differential Equations by : Uri Elias
Download or read book Oscillation Theory of Two-Term Differential Equations written by Uri Elias and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included.
Book Synopsis Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations by : R.P. Agarwal
Download or read book Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Oscillation, Nonoscillation, Stability and Asymptotic Properties for Second and Higher Order Functional Differential Equations by : Leonid Berezansky
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 488 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.
Book Synopsis Oscillation Theory of Delay Differential Equations by : I. Győri
Download or read book Oscillation Theory of Delay Differential Equations written by I. Győri and published by Clarendon Press. This book was released on 1991 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a resurgence of interest in the study of delay differential equations motivated largely by new applications in physics, biology, ecology, and physiology. The aim of this monograph is to present a reasonably self-contained account of the advances in the oscillation theory of this class of equations. Throughout, the main topics of study are shown in action, with applications to such diverse problems as insect population estimations, logistic equations in ecology, the survival of red blood cells in animals, integro-differential equations, and the motion of the tips of growing plants. The authors begin by reviewing the basic theory of delay differential equations, including the fundamental results of existence and uniqueness of solutions and the theory of the Laplace and z-transforms. Little prior knowledge of the subject is required other than a firm grounding in the main techniques of differential equation theory. As a result, this book provides an invaluable reference to the recent work both for mathematicians and for all those whose research includes the study of this fascinating class of differential equations.
Book Synopsis Oscillation Theory Of Partial Differential Equations by : Yoshida Norio
Download or read book Oscillation Theory Of Partial Differential Equations written by Yoshida Norio and published by World Scientific Publishing Company. This book was released on 2008-10-13 with total page 340 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.
Book Synopsis Bifurcation Theory of Functional Differential Equations by : Shangjiang Guo
Download or read book Bifurcation Theory of Functional Differential Equations written by Shangjiang Guo and published by Springer Science & Business Media. This book was released on 2013-07-30 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).
Book Synopsis Oscillation Theory for Second Order Dynamic Equations by : Ravi P. Agarwal
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
Book Synopsis Oscillation Theory Of Operator-differential Equations by : Drumi D Bainov
Download or read book Oscillation Theory Of Operator-differential Equations written by Drumi D Bainov and published by World Scientific. This book was released on 1995-08-31 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors aim at expounding a sufficiently rich oscillation theory and asymptotic theory of operator-differential equations. This book will be of interest not only to mathematicians, but also to experts in other areas of science and technology due to the numerous applications of the results discussed in the book.
Book Synopsis Half-Linear Differential Equations by : Ondrej Dosly
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.
Book Synopsis Nonlinear Analysis by : Leszek Gasinski
Download or read book Nonlinear Analysis written by Leszek Gasinski and published by CRC Press. This book was released on 2005-07-27 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.
Book Synopsis Oscillation Theory of Differential Equations with Deviating Arguments by : G. S. Ladde
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:
Book Synopsis Generalized Solutions of Functional Differential Equations by : Joseph Wiener
Download or read book Generalized Solutions of Functional Differential Equations written by Joseph Wiener and published by World Scientific. This book was released on 1993 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need to investigate functional differential equations with discontinuous delays is addressed in this book. Recording the work and findings of several scientists on differential equations with piecewise continuous arguments over the last few years, this book serves as a useful source of reference. Great interest is placed on discussing the stability, oscillation and periodic properties of the solutions. Considerable attention is also given to the study of initial and boundary-value problems for partial differential equations of mathematical physics with discontinuous time delays. In fact, a large part of the book is devoted to the exploration of differential and functional differential equations in spaces of generalized functions (distributions) and contains a wealth of new information in this area. Each topic discussed appears to provide ample opportunity for extending the known results. A list of new research topics and open problems is also included as an update.
