Geodesic
Some Elementary Converse Problems in Ordinary Differential Equations*
Canadian mathematical bulletin, Tome 11 (1968) no. 5, pp. 703-716

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Seminar, D. E. Some Elementary Converse Problems in Ordinary Differential Equations*. Canadian mathematical bulletin, Tome 11 (1968) no. 5, pp. 703-716. doi: 10.4153/CMB-1968-084-0
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