Differential and Integral Inequalities /

Differential and Integral Inequalities / by Wolfgang Walter.

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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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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Walter, Wolfgang
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 1970.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete ; n.F., Heft 55.
Subjects:
Mathematics.
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. Existence Theorems Based on the Line Method
  • Appendix Elliptic Differential Equations
  • List of Symbols
  • Author Index.

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