UID:
almahu_9947366289402882
Format:
1 online resource (399 p.)
ISBN:
1-282-28960-8
,
9786612289606
,
0-08-095618-1
Series Statement:
Mathematics in science and engineering ; v. 109
Content:
An introduction to nonlinear boundary value problems
Note:
Description based upon print version of record.
,
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)
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1.13. Existence in the Large for Systems1.14. 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
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3.1. Solution Funnels3.2. 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
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4.10. Leray Schauder's Alternative4.11. 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
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5.8. Notes and CommentsChapter 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
,
English
Additional Edition:
ISBN 0-12-093150-8
Language:
English
