Classical methods in ordinary differential equations : with applications to boundary value problem / Stuart P. Hastings, J. Bryce McLeod.

Format:

Book

Author/Creator:

Hastings, Stuart P., 1937- author.

McLeod, J. Bryce, 1929-2014, author.

Series:

Graduate studies in mathematics ; Volume 129.

Graduate Studies in Mathematics ; Volume 129

Language:

English

Subjects (All):

Boundary value problems.

Differential equations, Nonlinear.

Physical Description:

1 online resource (373 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

Language Note:

English

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. 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.

Contents:

""Shooting with more parameters""""Some problems of A. C. Lazer""; ""Chaotic motion of a pendulum""; ""Layers and spikes in reaction-diffusion equations, I""; ""Uniform expansions for a class of second order problems""; ""Layers and spikes in reaction-diffusion equations, II""; ""Three unsolved problems""; ""Bibliography""; ""Index""; ""Back Cover""

Notes:

"Applied Mathematics"--Cover.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-8218-8485-9