On The Asymptotic Behavior Of Solutions To Perturbed Linear Differential Equations

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Half-Linear Differential Equations

Author : Ondrej Dosly
Publisher : Elsevier
ISBN 13 : 0080461239
Total Pages : 533 pages
Book Rating : 4.0/5 (84 download)

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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-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.

Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations

Author : Ivan Kiguradze
Publisher : Springer Science & Business Media
ISBN 13 : 9401118086
Total Pages : 343 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations by : Ivan Kiguradze

Download or read book Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations written by Ivan Kiguradze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of solutions are established, and some general theorems on the classification of equations according to their oscillatory properties are proved. In addition, the conditions are found under which nonlinear equations do not have singular, proper, oscillatory and monotone solutions. The book has five chapters: Chapter I deals with linear differential equations; Chapter II with quasilinear equations; Chapter III with general nonlinear differential equations; and Chapter IV and V deal, respectively, with higher-order and second-order differential equations of the Emden-Fowler type. Each section contains problems, including some which presently remain unsolved. The volume concludes with an extensive list of references. For researchers and graduate students interested in the qualitative theory of differential equations.

Singular Perturbations and Asymptotics

Author : Richard E. Meyer
Publisher : Academic Press
ISBN 13 : 1483264572
Total Pages : 418 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Singular Perturbations and Asymptotics by : Richard E. Meyer

Download or read book Singular Perturbations and Asymptotics written by Richard E. Meyer and published by Academic Press. This book was released on 2014-05-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics. The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications. The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations. The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.

Introduction to Singular Perturbations

Author : Robert E. Jr. O'Malley
Publisher : Elsevier
ISBN 13 : 0323162274
Total Pages : 215 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Introduction to Singular Perturbations by : Robert E. Jr. O'Malley

Download or read book Introduction to Singular Perturbations written by Robert E. Jr. O'Malley and published by Elsevier. This book was released on 2012-12-02 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.

Asymptotic Integration of Differential and Difference Equations

Author : Sigrun Bodine
Publisher : Springer
ISBN 13 : 331918248X
Total Pages : 411 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Asymptotic Integration of Differential and Difference Equations by : Sigrun Bodine

Download or read book Asymptotic Integration of Differential and Difference Equations written by Sigrun Bodine and published by Springer. This book was released on 2015-05-26 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.

Singular-Perturbation Theory

Author : Donald R. Smith
Publisher : Cambridge University Press
ISBN 13 : 9780521300421
Total Pages : 532 pages
Book Rating : 4.3/5 (4 download)

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Book Synopsis Singular-Perturbation Theory by : Donald R. Smith

Download or read book Singular-Perturbation Theory written by Donald R. Smith and published by Cambridge University Press. This book was released on 1985-08-30 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to singular perturbation problems. Since the nature of the nonuniformity can vary from case to case, the author considers and solves a variety of problems, mostly for ordinary differential equations.

Differential and Integral Inequalities: Theory and Applications

Author : V. Lakshmikantham
Publisher : Academic Press
ISBN 13 : 0080955630
Total Pages : 405 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Differential and Integral Inequalities: Theory and Applications by : V. Lakshmikantham

Download or read book Differential and Integral Inequalities: Theory and Applications written by V. Lakshmikantham and published by Academic Press. This book was released on 1969 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applicationsof differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.

Asymptotic Behavior and Stability Problems in Ordinary Differential Equations

Author : Lamberto Cesari
Publisher : Springer Science & Business Media
ISBN 13 : 3642856713
Total Pages : 282 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari

Download or read book Asymptotic Behavior and Stability Problems in Ordinary Differential Equations written by Lamberto Cesari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call" qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.

Introduction to the General Theory of Singular Perturbations

Author : S. A. Lomov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897416
Total Pages : 402 pages
Book Rating : 4.8/5 (974 download)

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Book Synopsis Introduction to the General Theory of Singular Perturbations by : S. A. Lomov

Download or read book Introduction to the General Theory of Singular Perturbations written by S. A. Lomov and published by American Mathematical Soc.. This book was released on with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.

Technical Abstract Bulletin

Author :
Publisher :
ISBN 13 :
Total Pages : 866 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Technical Abstract Bulletin by :

Download or read book Technical Abstract Bulletin written by and published by . This book was released on 1967 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 654 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1965 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Analysis

Author : R. V. Gamkrelidze
Publisher : Springer Science & Business Media
ISBN 13 : 1468433032
Total Pages : 223 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Mathematical Analysis by : R. V. Gamkrelidze

Download or read book Mathematical Analysis written by R. V. Gamkrelidze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains three articles: "Asymptotic methods in the theory of ordinary differential equations" b'y V. F. Butuzov, A. B. Vasil'eva, and M. V. Fedoryuk, "The theory of best ap proximation in Dormed linear spaces" by A. L. Garkavi, and "Dy namical systems with invariant measure" by A. 'VI. Vershik and S. A. Yuzvinskii. The first article surveys the literature on linear and non linear singular asymptotic problems, in particular, differential equations with a small parameter. The period covered by the survey is primarily 1962-1967. The second article is devoted to the problem of existence, characterization, and uniqueness of best approximations in Banach spaces. One of the chapters also deals with the problem of the convergence of positive operators, inasmuch as the ideas and methods of this theory are close to those of the theory of best ap proximation. The survey covers the literature of the decade 1958-1967. The third article is devoted to a comparatively new and rapid ly growing branch of mathematics which is closely related to many classical and modern mathematical disciplines. A survey is given of results in entropy theory, classical dynamic systems, ergodic theorems, etc. The results surveyed were primarily published during the period 1956-1967.

Canadian Mathematical Bulletin

Author :
Publisher :
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4./5 ( download)

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Book Synopsis Canadian Mathematical Bulletin by :

Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1965 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Research in Progress

Author :
Publisher :
ISBN 13 :
Total Pages : 834 pages
Book Rating : 4.:/5 (334 download)

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Book Synopsis Research in Progress by :

Download or read book Research in Progress written by and published by . This book was released on 1978 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Index of Mathematical Papers

Author :
Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Index of Mathematical Papers by :

Download or read book Index of Mathematical Papers written by and published by . This book was released on 1974 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 1282 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1982 with total page 1282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Functional Differential Equations

Author : J. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 1461599687
Total Pages : 247 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Functional Differential Equations by : J. Hale

Download or read book Functional Differential Equations written by J. Hale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is hoped that these notes will serve as an introduction to the subject of functional differential equations. The topics are very selective and represent only one particular viewpoint. Complementary material dealing with extensions of closely related topics are given in the notes at the end. A short bibliography is appended as source material for further study. The author is very grateful to the Mathematics Department at UCLA for having extended the invitation to give a series of lectures on functional differ ential equations during the Applied Mathematics Year, 1968-1969. The extreme interest and sincere criticism of the members of the audience were a constant source of inspiration in the preparation of the lectures as well as the notes. Except for Sections 6, 32, 33, 34 and some other minor modifications, the notes represent the material covered in two quarters at UCLA. The author wishes to thank Katherine McDougall and Sandra Spinacci for their excellent preparation of the text. The author is also indebted to Eleanor Addison for her work on the drawings and to Dr. H. T. Banks for his careful proofreading of this material. Jack K. Hale Providence March 4, 1971 v TABLE OF CONTENTS 1. INTRODUCTION •••••.•..••.•••••••••.•••..•.••••••.••••••.••.••.•••.••• 1 2 • A GENERAL INITIAL VALUE PROBLEM 11 3 • EXISTENCE 13 4. CONTINUATION OF SOLUTIONS 16 CONTINUOUS DEPENDENCE AND UNIQUENESS 21 5.