Global Solution Branches of Two Point Boundary Value Problems
Schaaf, Renate.
Global Solution Branches of Two Point Boundary Value Problems [electronic resource] / by Renate Schaaf. - XXII, 146 p. online resource. - Lecture Notes in Mathematics, 1458 0075-8434 ; . - Lecture Notes in Mathematics, 1458 .
Dirichlet branches bifurcating from zero -- Neumann problems, period maps and semilinear dirichlet problems -- Generalizations -- General properties of time maps.
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.
9783540467427
10.1007/BFb0098346 doi
Global analysis (Mathematics).
Analysis.
QA299.6-433
515
Global Solution Branches of Two Point Boundary Value Problems [electronic resource] / by Renate Schaaf. - XXII, 146 p. online resource. - Lecture Notes in Mathematics, 1458 0075-8434 ; . - Lecture Notes in Mathematics, 1458 .
Dirichlet branches bifurcating from zero -- Neumann problems, period maps and semilinear dirichlet problems -- Generalizations -- General properties of time maps.
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.
9783540467427
10.1007/BFb0098346 doi
Global analysis (Mathematics).
Analysis.
QA299.6-433
515