Global Solution Branches of Two Point Boundary Value Problems

✍ Scribed by Renate Schaaf (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1990
• Tongue: English
• Leaves: 159
• Series: Lecture Notes in Mathematics 1458
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Dirichlet branches bifurcating from zero....Pages 1-44
Neumann problems, period maps and semilinear dirichlet problems....Pages 45-68
Generalizations....Pages 69-109
General properties of time maps....Pages 110-136

✦ Subjects

Analysis