Differential and Integral Inequalities
In 1964 the author's mono graph "Differential- und Integral-Un gleichungen," with the subtitle "und ihre Anwendung bei Abschätzungs und Eindeutigkeitsproblemen" was published. The present volume grew out of the response to the demand for an English translation of this book...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1970, 1970
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| Edition: | 1st ed. 1970 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I Volterra.Integral Equations
- 1. Monotone Kernels
- 2. Remarks on the Existence Problem. Maximal and Minimal Solutions
- 3. Generalization of the Monotonicity Concept
- 4. Estimates and Uniqueness Theorems
- 5. Ordinary Differential Equations (in the Sense of Carathéodory)
- 6. Systems of Integral Equations
- 7. Bounds for Systems Using K-Norms
- II Ordinary Differential Equations
- 8. Basic Theorems on Differential Inequalities
- 9. Estimates for the Initial Value Problem for an Ordinary Differential Equation of First Order
- 10. Uniqueness Theorems
- 11. Systems of Ordinary Differential Equations. Estimation by K-Norms
- 12. Systems of Differential Inequalities
- 13. Component-wise Bounds for Systems
- 14. Further Uniqueness Results for Systems
- 15. Differential Equations of Higher Order
- 16. Supplement
- III Volterra Integral Equations in Several Variables Hyperbolic Differential Equations
- 17. Monotone Operators
- 18. Existence Theorems
- 19. Estimates for Integral Equations
- 20. The Hyperbolic Differential Equations uxy= f (x, y, u)
- 21. The Differential Equation uxy = f (x, y, u, ux, uy)
- 22. Supplements. The Local Method of Proof
- IV Parabolic Differential Equations
- 23. Notation
- 24. The Nagumo-Westphal Lemma
- 25. The First Boundary Value Problem
- 26. The Maximum-Minimum Principle
- 27. The Shape of Profiles
- 28. Infinite Domains, Discontinuous Initial Values, Problems Without Initial Values
- 29. Heat Conduction as an Example
- 30. Application to Boundary Layer Theory
- 31. The Third Boundary Value Problem
- 32. Systems of Parabolic Differential Equations
- 33. Uniqueness Problems for Parabolic Systems
- 34. Generalizations and Supplements. The Nonstationary Boundary Layer Equations
- 35. The Line Method for Parabolic Equations
- 36. ExistenceTheorems Based on the Line Method
- Appendix Elliptic Differential Equations
- List of Symbols
- Author Index