Existence Theory For Nonlinear Ordinary Differential Equations
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Existence Theory For Nonlinear Ordinary Differential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
Existence Theory For Nonlinear Ordinary Differential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer
Release Date : 2014-03-14
Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-14 with Mathematics categories.
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
Existence Theory For Nonlinear Integral And Integrodifferential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Existence Theory For Nonlinear Integral And Integrodifferential Equations written by Donal O'Regan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theory of integral and integrodifferential equations has ad vanced rapidly over the last twenty years. Of course the question of existence is an age-old problem of major importance. This mono graph is a collection of some of the most advanced results to date in this field. The book is organized as follows. It is divided into twelve chap ters. Each chapter surveys a major area of research. Specifically, some of the areas considered are Fredholm and Volterra integral and integrodifferential equations, resonant and nonresonant problems, in tegral inclusions, stochastic equations and periodic problems. We note that the selected topics reflect the particular interests of the authors. Donal 0 'Regan Maria Meehan CHAPTER 1 INTRODUCTION AND PRELIMINARIES 1.1. Introduction The aim of this book is firstly to provide a comprehensive existence the ory for integral and integrodifferential equations, and secondly to present some specialised topics in integral equations which we hope will inspire fur ther research in the area. To this end, the first part of the book deals with existence principles and results for nonlinear, Fredholm and Volterra inte gral and integrodifferential equations on compact and half-open intervals, while selected topics (which reflect the particular interests of the authors) such as nonresonance and resonance problems, equations in Banach spaces, inclusions, and stochastic equations are presented in the latter part.
Nonlinear Ordinary Differential Equations
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Author : Dominic Jordan
language : en
Publisher: OUP Oxford
Release Date : 2007-08-24
Nonlinear Ordinary Differential Equations written by Dominic Jordan and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-24 with Mathematics categories.
This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007). Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.
Basic Theory Of Ordinary Differential Equations
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Author : Po-Fang Hsieh
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Basic Theory Of Ordinary Differential Equations written by Po-Fang Hsieh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The authors' aim is to provide the reader with the very basic knowledge necessary to begin research on differential equations with professional ability. The selection of topics should provide the reader with methods and results that are applicable in a variety of different fields. The text is suitable for a one-year graduate course, as well as a reference book for research mathematicians. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history. The book has 114 illustrations and 206 exercises. Hints and comments for many problems are given.
Integral And Integrodifferential Equations
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Author : Ravi P. Agarwal
language : en
Publisher: CRC Press
Release Date : 2000-03-09
Integral And Integrodifferential Equations written by Ravi P. Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-09 with Mathematics categories.
This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.
Introduction To Nonlinear Differential And Integral Equations
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Author : Harold Thayer Davis
language : en
Publisher:
Release Date : 1960
Introduction To Nonlinear Differential And Integral Equations written by Harold Thayer Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Calculus categories.
Nonlinear Ordinary Differential Equations
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Author : R. Grimshaw
language : en
Publisher: Routledge
Release Date : 2017-10-19
Nonlinear Ordinary Differential Equations written by R. Grimshaw and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.
Ordinary Differential Equations And Stability Theory
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Author : David A. Sanchez
language : en
Publisher: Courier Dover Publications
Release Date : 2019-09-18
Ordinary Differential Equations And Stability Theory written by David A. Sanchez and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-18 with Mathematics categories.
This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.
A Textbook On Ordinary Differential Equations
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Author : Shair Ahmad
language : en
Publisher: Springer
Release Date : 2015-06-05
A Textbook On Ordinary Differential Equations written by Shair Ahmad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-05 with Mathematics categories.
This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.