Description
Book SynopsisPresents rigorous 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.
Table of ContentsIntroduction 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
