Author: Renate Schaaf
Publisher: Springer
ISBN: 3540467424
Category : Mathematics
Languages : en
Pages : 160
Book Description
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.
Global Solution Branches of Two Point Boundary Value Problems
Author: Renate Schaaf
Publisher: Springer
ISBN: 3540467424
Category : Mathematics
Languages : en
Pages : 160
Book Description
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.
Publisher: Springer
ISBN: 3540467424
Category : Mathematics
Languages : en
Pages : 160
Book Description
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 Solution of Two Point Boundary Value Problems
Author: Herbert B. Keller
Publisher: SIAM
ISBN: 9781611970449
Category : Mathematics
Languages : en
Pages : 69
Book Description
Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
Publisher: SIAM
ISBN: 9781611970449
Category : Mathematics
Languages : en
Pages : 69
Book Description
Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
Numerical Methods for Two-Point Boundary-Value Problems
Author: Herbert B. Keller
Publisher: Courier Dover Publications
ISBN: 0486828344
Category : Mathematics
Languages : en
Pages : 417
Book Description
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.
Publisher: Courier Dover Publications
ISBN: 0486828344
Category : Mathematics
Languages : en
Pages : 417
Book Description
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: 0080462472
Category : Mathematics
Languages : en
Pages : 502
Book Description
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
Publisher: Elsevier
ISBN: 0080462472
Category : Mathematics
Languages : en
Pages : 502
Book Description
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
Numerical Solution of Two Point Boundary Value Problems
Author: Herbert B. Keller
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 61
Book Description
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 61
Book Description
Nonlinear Two Point Boundary Value Problems
Author: Bailey
Publisher: Academic Press
ISBN: 0080955525
Category : Computers
Languages : en
Pages : 190
Book Description
Nonlinear Two Point Boundary Value Problems
Publisher: Academic Press
ISBN: 0080955525
Category : Computers
Languages : en
Pages : 190
Book Description
Nonlinear Two Point Boundary Value Problems
Nonlinear Analysis and its Applications to Differential Equations
Author: M.R. Grossinho
Publisher: Springer Science & Business Media
ISBN: 1461201918
Category : Mathematics
Languages : en
Pages : 383
Book Description
This work, consisting of expository articles as well as research papers, highlights recent developments in nonlinear analysis and differential equations. The material is largely an outgrowth of autumn school courses and seminars held at the University of Lisbon and has been thoroughly refereed. Several topics in ordinary differential equations and partial differential equations are the focus of key articles, including: * periodic solutions of systems with p-Laplacian type operators (J. Mawhin) * bifurcation in variational inequalities (K. Schmitt) * a geometric approach to dynamical systems in the plane via twist theorems (R. Ortega) * asymptotic behavior and periodic solutions for Navier--Stokes equations (E. Feireisl) * mechanics on Riemannian manifolds (W. Oliva) * techniques of lower and upper solutions for ODEs (C. De Coster and P. Habets) A number of related subjects dealing with properties of solutions, e.g., bifurcations, symmetries, nonlinear oscillations, are treated in other articles. This volume reflects rich and varied fields of research and will be a useful resource for mathematicians and graduate students in the ODE and PDE community.
Publisher: Springer Science & Business Media
ISBN: 1461201918
Category : Mathematics
Languages : en
Pages : 383
Book Description
This work, consisting of expository articles as well as research papers, highlights recent developments in nonlinear analysis and differential equations. The material is largely an outgrowth of autumn school courses and seminars held at the University of Lisbon and has been thoroughly refereed. Several topics in ordinary differential equations and partial differential equations are the focus of key articles, including: * periodic solutions of systems with p-Laplacian type operators (J. Mawhin) * bifurcation in variational inequalities (K. Schmitt) * a geometric approach to dynamical systems in the plane via twist theorems (R. Ortega) * asymptotic behavior and periodic solutions for Navier--Stokes equations (E. Feireisl) * mechanics on Riemannian manifolds (W. Oliva) * techniques of lower and upper solutions for ODEs (C. De Coster and P. Habets) A number of related subjects dealing with properties of solutions, e.g., bifurcations, symmetries, nonlinear oscillations, are treated in other articles. This volume reflects rich and varied fields of research and will be a useful resource for mathematicians and graduate students in the ODE and PDE community.
Global Solution Curves For Semilinear Elliptic Equations
Author: Philip Korman
Publisher: World Scientific
ISBN: 9814458066
Category : Mathematics
Languages : en
Pages : 254
Book Description
This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented.The author is one of the original contributors to the field of exact multiplicity results.
Publisher: World Scientific
ISBN: 9814458066
Category : Mathematics
Languages : en
Pages : 254
Book Description
This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented.The author is one of the original contributors to the field of exact multiplicity results.
Handbook of Differential Equations: Ordinary Differential Equations
Author: A. Canada
Publisher: Elsevier
ISBN: 0080463819
Category : Mathematics
Languages : en
Pages : 753
Book Description
This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields
Publisher: Elsevier
ISBN: 0080463819
Category : Mathematics
Languages : en
Pages : 753
Book Description
This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields
Two-point Boundary Value Problems: Shooting Methods
Author: Sanford M. Roberts
Publisher: Elsevier Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 300
Book Description
Publisher: Elsevier Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 300
Book Description