An Introduction to Nonlinear Boundary Value Problems
Published on 14. May 2014
399 pages
978-0-08-095618-3 (ISBN)
Description
A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed:
- methods that involve differential inequalities;
- shooting and angular function techniques;
- functional analytic approaches;
- topological methods.
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095618-3 (9780080956183)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
S.R. Bernfeld | V. Lakshmikantham
Introduction to Nonlinear Boundary Value Problems
Book
01/1974
Academic Press
€81.09
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Content
- Front Cover
- An Introduction to Nonlinear Boundary Value Problems
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Chapter 1. Methods Involving Differential Inequalities
- 1.0. Introduction
- 1.1. Existencein the small
- 1.2. Upper and Lower Solutions
- 1.3. The Modified Function
- 1.4. Nagumo's Condition
- 1.5. Existence in the Large
- 1.6. Lyapunov-Like Functions
- 1.7. Existence on Infinite Intervals
- 1.8. Super- and Subfunctions
- 1.9. Properties of Subfunctions
- 1.10. Perron's Method
- 1.11. Modified Vector Function
- 1.12. Nagumo's Condition (Continued)
- 1.13. Existence in the Large for Systems
- 1.14. Further Results for Systems
- 1.15. Notes and comments
- Chapter 2. Shooting Type Methods
- 2.0. Introduction
- 2.1. Uniqueness Implies Existence
- 2.2. General Linear Boundary Conditions
- 2.3. Weaker Uniqueness Conditions
- 2.4. Nonlinear Boundary Conditions
- 2.5. Angular Function Technique
- 2.6. Fundamental Lemmas
- 2.7. Existence
- 2.8. Uniqueness
- 2.9. Estimation of Number of Solutions
- 2.10. Existence of Infinite Number of Solutions
- 2.11. Nonlinear Boundary Conditions
- 2.12. Notes and Comments
- Chapter 3. Topological Methods
- 3.0. Introduction
- 3.1. Solution Funnels
- 3.2. Application to Second-Order Equations
- 3.3. Wazewski Retract Method
- 3.4. Generalized Differential Equations
- 3.5. Dependence of Solutions on Boundary Data
- 3.6. Notes and Comments
- Chapter 4. Functional Analytic Methods
- 4.0. Introduction
- 4.1. Linear Problems for Linear Systems
- 4.2. Linear Problems for Nonlinear Systems
- 4.3. Interpolation Problems
- 4.4. Further Nonlinear Problems
- 4.5. Generalized Spaces
- 4.6. Integral Equations
- 4.7. Application to Existence and Uniqueness
- 4.8. Method of A Priori Estimates
- 4.9. Bounds for Solutions in Admissible Subspaces
- 4.10. Leray Schauder's Alternative
- 4.11. Application of Leray-Schauder's Alternative
- 4.12. Periodic Boundary Conditions
- 4.13. Set-Valued Mappings and Functional Equations
- 4.14. General Linear Problems
- 4.15. General Results for Set-Valued Mappings
- 4.16. Set-Valued Differential Equations
- 4.17. Notes and Comments
- Chapter 5. Extensions to Functional Differential Equations
- 5.0. Introduction
- 5.1. Existence in the Small
- 5.2. Existence in the Large
- 5.3. Shooting Method
- 5.4. Nonhomogeneous Linear Boundary Conditions
- 5.5. Linear Problems
- 5.6. Nonlinear Problems
- 5.7. Degenerate Cases
- 5.8. Notes and Comments
- Chapter 6. Selected Topics
- 6.0. Introduction
- 6.1. Newton's Method
- 6.2. The Goodman-Lance Method
- 6.3. The Method of Quasilinearization
- 6.4. Nonlinear Eigenvalue Problems
- 6.5. n-Parameter Families and Interpolation Problems
- 6.6. Notes and Comments
- Bibliography
- Additional Bibliography
- Index
