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Some Elementary Converse Problems in Ordinary Differential Equations*

Published online by Cambridge University Press:  20 November 2018

D. E. Seminar
D. E. Seminar*
Affiliation:
Aarhus University, Denmark, York University, Toronto
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In studying differential equations, the usual task is to determine properties of the solutions of such equations from a knowledge of the coefficient functions. The converse question, namely, of determining the coefficient functions from properties of solutions, also has significance. It has been studied especially in the case of Sturm-Liouville equations.

A discussion of the inverse Sturm-Liouville problem can be found in [8, Chapter 8], where references are given to the work of W.A. Ambarzumiam, G. Borg, I.M. Gelfand, M.G. Krein, B.M. Levitan, N. Levinson and W.A. Marchenko on this problem. Work of a quite different character, but dealing also with questions of a converse type arising from Sturm-Liouville equations, has been done by O. Boruvka and his colleagues and students [2].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 5 , December 1968 , pp. 703 - 716
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

*

The results arose from discussions in a seminar on differential equations at Aarhus University, Denmark, during 1964-65. The participants were JɈtte Bretlau, Villy K. Christensen, Jens Jørgen Hoist, Margrethe Jørgensen, Tove Lund Jørgensen, Karen Skov Larsen, Lee Lorch, Niels Wendell Pedersen, Per Amdal Steffensen, Leif Hautop Sørensen, and Preben Dahl Vestergaard.

References

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