De Coster, Colette.
Two-point boundary value problems : lower and upper solutions / Colette De Coster, Patrick Habets. - 1st ed. - 1 online resource (x, 489 pages) - Mathematics in science and engineering, v. 205 0076-5392 ; . - Mathematics in science and engineering ; v. 205. .
Includes bibliographical references (p. 463-487) and index.
Preface -- Notations -- Introduction -- The History -- I. The Periodic Problem -- II. The Separated BVP -- III. Relation with Degree Theory -- IV. Variational Methods -- V. Monotone Iterative Methods -- VI. Parametric Multiplicity Problems -- VII. Resonance and Nonresonance -- VIII. Positive Solutions -- IX. Problem with Singular Forces -- X. Singular Perturbations -- XI. Bibliographical Notes -- Appendix -- Bibliography -- Index.
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.
9780444522009 044452200X 0080462472 (electronic bk.) 9780080462479 (electronic bk.)
131843:131950 Elsevier Science & Technology http://www.sciencedirect.com
Boundary value problems.
Functional differential equations.
MATHEMATICS--Differential Equations--General.
Boundary value problems.
Functional differential equations.
Electronic books.
QA379 / .D4 2006eb
515/.35
Two-point boundary value problems : lower and upper solutions / Colette De Coster, Patrick Habets. - 1st ed. - 1 online resource (x, 489 pages) - Mathematics in science and engineering, v. 205 0076-5392 ; . - Mathematics in science and engineering ; v. 205. .
Includes bibliographical references (p. 463-487) and index.
Preface -- Notations -- Introduction -- The History -- I. The Periodic Problem -- II. The Separated BVP -- III. Relation with Degree Theory -- IV. Variational Methods -- V. Monotone Iterative Methods -- VI. Parametric Multiplicity Problems -- VII. Resonance and Nonresonance -- VIII. Positive Solutions -- IX. Problem with Singular Forces -- X. Singular Perturbations -- XI. Bibliographical Notes -- Appendix -- Bibliography -- Index.
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.
9780444522009 044452200X 0080462472 (electronic bk.) 9780080462479 (electronic bk.)
131843:131950 Elsevier Science & Technology http://www.sciencedirect.com
Boundary value problems.
Functional differential equations.
MATHEMATICS--Differential Equations--General.
Boundary value problems.
Functional differential equations.
Electronic books.
QA379 / .D4 2006eb
515/.35