Jack K. Hale's Books

Ordinary Differential Equations

By: Jack K. Hale

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Ordinary Differential Equations

By: Jack K. Hale

This rigorous treatment prepares readers for the study of differential equations and shows them how to research current literature. It emphasizes nonlinear problems and specific analytical methods. 1969 edition.

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Page Count

386

Publisher

Courier Corporation

Published Date

ISBN 10

0486472116

ISBN 13

9780486472119

Topics in Dynamic Bifurcation Theory

By: Jack K. Hale

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Topics in Dynamic Bifurcation Theory

By: Jack K. Hale

Presents the general theory of first order bifurcation that occur for vector fields in finite dimensional space. This book includes formulation of structural stability and bifurcation in infinite dimensions.

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American Mathematical Soc.

Published Date

ISBN 10

0821816985

ISBN 13

9780821816981

Oscillations in Nonlinear Systems

By: Jack K. Hale

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Oscillations in Nonlinear Systems

By: Jack K. Hale

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction provides a unified approach for obtaining periodic solutions to nonautonomous and autonomous differential equations. 1963 edition.

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193

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486803260

ISBN 13

9780486803265

Oscillation and Dynamics in Delay Equations

Proceedings of an AMS Special Session Held January 16-19, 1991

By: John R. Graef,Jack K. Hale,American Mathematical Society. Meeting

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Oscillation and Dynamics in Delay Equations

Proceedings of an AMS Special Session Held January 16-19, 1991

By: John R. Graef,Jack K. Hale,American Mathematical Society. Meeting

Oscillation theory and dynamical systems have long been rich and active areas of research. Containing frontier contributions by some of the leaders in the field, this book brings together papers based on presentations at the AMS meeting in San Francisco in January 1991. With special emphasis on delay equations, the papers cover a broad range of topics in ordinary, partial, and difference equations and include applications to problems in commodity prices, biological modelling, and number theory. The book would be of interest to graduate students and researchers in mathematics or those in other fields who have an interest in delay equations and their applications.

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Page Count

274

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851403

ISBN 13

9780821851401

Theory of Functional Differential Equations

By: Jack K. Hale

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Theory of Functional Differential Equations

By: Jack K. Hale

Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.

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374

Publisher

Springer Science & Business Media

Published Date

ISBN 10

146129892X

ISBN 13

9781461298922

Dynamics in Infinite Dimensions

By: Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva

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Dynamics in Infinite Dimensions

By: Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva

State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

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Page Count

286

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387228969

ISBN 13

9780387228969

Asymptotic Behavior of Dissipative Systems

By: Jack K. Hale

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Asymptotic Behavior of Dissipative Systems

By: Jack K. Hale

This monograph reports the advances that have been made in the area by the author and many other mathematicians; it is an important source of ideas for the researchers interested in the subject. --Zentralblatt MATH Although advanced, this book is a very good introduction to the subject, and the reading of the abstract part, which is elegant, is pleasant. ... this monograph will be of valuable interest for those who aim to learn in the very rapidly growing subject of infinite-dimensional dissipative dynamical systems. --Mathematical Reviews This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor.

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Page Count

210

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821849344

ISBN 13

9780821849347

Introduction to Functional Differential Equations

By: Jack K. Hale,Sjoerd M. Verduyn Lunel

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Introduction to Functional Differential Equations

By: Jack K. Hale,Sjoerd M. Verduyn Lunel

The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constants formula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .

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458

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Springer Science & Business Media

Published Date

ISBN 10

1461243424

ISBN 13

9781461243427

Ordinary Differential Equations

By: Jack K. Hale

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Ordinary Differential Equations

By: Jack K. Hale

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386

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Courier Corporation

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ISBN 10

0486472116

ISBN 13

9780486472119

Dynamics and Bifurcations

By: Jack K. Hale,Hüseyin Kocak

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Dynamics and Bifurcations

By: Jack K. Hale,Hüseyin Kocak

In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.

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577

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Springer Science & Business Media

Published Date

ISBN 10

1461244269

ISBN 13

9781461244264

Introduction to Functional Differential Equations

By: Jack K. Hale,Sjoerd M. Verduyn Lunel

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Introduction to Functional Differential Equations

By: Jack K. Hale,Sjoerd M. Verduyn Lunel

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Page Count

476

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387940766

ISBN 13

9780387940762

Book's by Jack K. Hale

Ordinary Differential Equations

Ordinary Differential Equations

Topics in Dynamic Bifurcation Theory

Topics in Dynamic Bifurcation Theory

Oscillations in Nonlinear Systems

Oscillations in Nonlinear Systems

Oscillation and Dynamics in Delay Equations

Oscillation and Dynamics in Delay Equations

Theory of Functional Differential Equations

Theory of Functional Differential Equations

Dynamics in Infinite Dimensions

Dynamics in Infinite Dimensions

Asymptotic Behavior of Dissipative Systems

Asymptotic Behavior of Dissipative Systems

Introduction to Functional Differential Equations

Introduction to Functional Differential Equations

Ordinary Differential Equations

Ordinary Differential Equations

Dynamics and Bifurcations

Dynamics and Bifurcations

Introduction to Functional Differential Equations

Introduction to Functional Differential Equations

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