Author | Walter, Wolfgang. author |
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Title | Differential and Integral Inequalities [electronic resource] / by Wolfgang Walter |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1970 |
Connect to | http://dx.doi.org/10.1007/978-3-642-86405-6 |
Descript | X, 354 p. 14 illus. online resource |
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 Carathรฉodory) -- 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