Global Solution Branches of Two Point Boundary Value Problems

Author: Renate Schaaf
Publisher: Springer
ISBN: 3540467424
Format: PDF, ePub
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The book deals with parameter dependent problems of the form u"+*f(u)=0 on an interval with homogeneous Dirichlet or Neuman boundary conditions. These problems have a family of solution curves in the (u,*)-space. By examining the so-called time maps of the problem the shape of these curves is obtained which in turn leads to information about the number of solutions, the dimension of their unstable manifolds (regarded as stationary solutions of the corresponding parabolic prob- lem) as well as possible orbit connections between them. The methods used also yield results for the period map of certain Hamiltonian systems in the plane. The book will be of interest to researchers working in ordinary differential equations, partial differential equations and various fields of applications. By virtue of the elementary nature of the analytical tools used it can also be used as a text for undergraduate and graduate students with a good background in the theory of ordinary differential equations.

Numerical Methods for Two Point Boundary Value Problems

Author: Herbert B. Keller
Publisher: Courier Dover Publications
ISBN: 0486828344
Format: PDF, ePub, Docs
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Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.

Two Point Boundary Value Problems Lower and Upper Solutions

Author: C. De Coster
Publisher: Elsevier
ISBN: 9780080462479
Format: PDF
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This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction. · Presents the fundamental features of the method · Construction of lower and upper solutions in problems · Working applications and illustrated theorems by examples · Description of the history of the method and Bibliographical notes