Classical methods in ordinary differential equations : with applications to boundary value problems
著者
書誌事項
Classical methods in ordinary differential equations : with applications to boundary value problems
（Graduate studies in mathematics, v. 129）
American Mathematical Society, c2012
- : hardback
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注記
"Applied mathematics"--Cover
Bibliography: p. 357-369
Includes index
内容説明・目次
内容説明
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.
目次
- 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 FitzHugh-Nagumo equations Singular perturbation problems--rigorous matching Asymptotics beyond all orders Some solutions of the Falkner-Skan 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 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
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