Classical methods in ordinary differential equations : with applications to boundary value problems
 Author/Creator
 Hastings, Stuart P., 1937
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xvii, 373 p. : ill ; 27 cm.
 Series
 Graduate studies in mathematics ; v. 129.
Access
Available online

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QA379 .H377 2012

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QA379 .H377 2012
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Contributors
 Contributor
 McLeod, J. Bryce, 19292014
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 357369) and index.
 Contents

 Introduction An introduction to shooting methods Some boundary value problems for the Painleve transcendents Periodic solutions of a higher order system A linear example Homoclinic orbits of the FitzHughNagumo equations Singular perturbation problemsrigorous matching Asymptotics beyond all orders Some solutions of the FalknerSkan equation Poiseuille flow: Perturbation and decay Bending of a tapered rod variational methods and shooting Uniqueness and multiplicity Shooting with more parameters Some problems of A. C. Lazer Chaotic motion of a pendulum Layers and spikes in reactiondiffusion equations, I Uniform expansions for a class of second order problems Layers and spikes in reactiondiffusion equations, II Three unsolved problems Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This text emphasises rigourous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behaviour of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or travelling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed. The book gives complete classical proofs, while also emphasising the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years.< /p> Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics. .
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Stuart P. Hastings, J. Bryce McLeod.
 Series
 Graduate studies in mathematics ; v. 129
 ISBN
 9780821846940
 0821846949