Two-Point Boundary Value Problems: Lower and Upper Solutions PDF Download
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Author: C. De Coster
Publisher: Elsevier
ISBN: 0080462472
Category : Mathematics
Languages : en
Pages : 502
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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
Author: C. De Coster
Publisher: Elsevier
ISBN: 0080462472
Category : Mathematics
Languages : en
Pages : 502
Get Book Here
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
Author: Herbert B. Keller
Publisher: SIAM
ISBN: 9781611970449
Category : Mathematics
Languages : en
Pages : 69
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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.
Author: Johann Schröder
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
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Book Description
Author: Bailey
Publisher: Academic Press
ISBN: 0080955525
Category : Computers
Languages : en
Pages : 190
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Book Description
Nonlinear Two Point Boundary Value Problems
Author: Herbert Bishop Keller
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 416
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Book Description
A brief, elementary yet rigorous account of practical numerical methods for solving very general two-point boundary-value problems. Advanced undergraduate level. Over 100 problems.
Author: J. Schroeder
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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Book Description
Author: Renate Schaaf
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 170
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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.
Author: Leslie Fox
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 392
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Book Description
Author: Vasile Staicu
Publisher: Springer Science & Business Media
ISBN: 3764384824
Category : Mathematics
Languages : en
Pages : 436
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Book Description
This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.
Author: Feliz Manuel Minhos
Publisher: World Scientific
ISBN: 9813220074
Category : Mathematics
Languages : en
Pages : 217
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Book Description
This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm-Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations). It also includes classical and new methods and techniques to deal with the lack of compactness of the related operators.The reader will find a selection of original and recent results in this field, conditions to obtain solutions with particular qualitative properties, such as homoclinic and heteroclinic solutions and its relation with the solutions of Lidstone problems on all the real line.Each chapter contains applications to real phenomena, to classical equations or problems, with a common denominator: they are defined on unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete cases.The last part features some higher order functional problems, which generalize the classical two-point or multi-point boundary conditions, to more comprehensive data where an overall behavior of the unknown functions and their derivatives is involved.
