Focal Boundary Value Problems for Differential and Difference Equations by R.P. AgarwalFocal Boundary Value Problems for Differential and Difference Equations by R.P. Agarwal

Focal Boundary Value Problems for Differential and Difference Equations

byR.P. Agarwal

Paperback | December 7, 2010

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This monograph presents an up-to-date account of the theory of right focal point boundary value problems for differential and difference equations. Topics include existence and uniqueness, Picard's method, quasilinearisation, necessary and sufficient conditions for right disfocality, right and eventual disfocalities, Green's functions, monotone convergence, continuous dependence and differentiation with respect to boundary values, infinite interval problems, best possible results, control theory methods, focal subfunctions, singular problems, and problems with impulse effects. Audience: This work will be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.
Title:Focal Boundary Value Problems for Differential and Difference EquationsFormat:PaperbackDimensions:303 pages, 10.98 × 8.27 × 0 inPublished:December 7, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048150051

ISBN - 13:9789048150052

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Table of Contents

Preface. 1: Continuous Problems. 1.1. Introduction. 1.2. Abel-Gontscharoff Interpolation. 1.3. Solution of Linear Problems. 1.4. Existence and Uniqueness. 1.5. Picard's and Approximate Picard's Methods. 1.6. Quasilinearization and Approximate Quasilinearization. 1.7. Integro-Differential Equations. 1.8. Delay-Differential Equations. 1.9. Necessary and Sufficient Conditions for Right Disfocality. 1.10. Tests for Right and Eventual Disfocalities. 1.11. Green's Functions. 1.12. Monotone Convergence. 1.13. Uniqueness Implies Uniqueness. 1.14. Uniqueness Implies Existence. 1.15. Continuous Dependence and Differentiation with respect to Boundary Values. 1.16. Right Disfocality Implies Right Disfocality. 1.17. Right Disfocality Implies Existence. 1.18. Differential Inequalities Imply Existence. 1.19. Infinite Interval Problems. 1.20. Best Possible Results: Control Theory Methods. 1.21. Converse Theorems. 1.22. Focal Subfunctions. 1.23. Generalized Problem I. 1.24. Generalized Problem II. 1.25. A Singular Problem. 1.26. A Problem with Impulse Effects. Comments and Remarks. References. 2: Discrete Problems. 2.1. Introduction. 2.2. Discrete Abel-Gontscharoff Interpolation. 2.3. Existence and Uniqueness. 2.4. Picard's and Approximate Picard's Methods. 2.5. Quasilinearization and Approximate Linearization. 2.6. Necessary and Sufficient Conditions for Right Disfocality. 2.7. Tests for Right and Eventual Disfocalities. 2.8. Green's Functions. 2.9. Monotone Convergence. 2.10. Continuous Dependence and Differentiation with Respect to Initial and Boundary Values. 2.11. Differences with Respect to Boundary Points. 2.12. Uniqueness Implies Existence. 2.13. Generalized Problems. Comments and Remarks. References. Index.

Editorial Reviews

`...will be useful for a graduate course concerned with boundary value problems for either differential equations or difference equations. It also would be an excellent book for mathematicians doing research in this area.' Mathematical Reviews, 99b