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This article is cited in 14 scientific papers (total in 14 papers)
On inverse nodal problem for Sturm-Liouville operator
A. Yu. Trynin Saratov State University, Saratov, Russia
Abstract:
In this paper we propose a solution to a certain inverse Sturm-Liouville problem, which allows one to determine the potential and the boundary conditions of the differential operator on the values of one of the differentials of Gateaux zeroes $ x_ {k, n} [q ] \in (0, \pi) $ of some eigenfunction $ \hat y (x, q, \lambda_n [q]) $ for an increment $ w $ from the set $ \mathbb W $. As $ \mathbb W $, we consider some sets of classical and generalized functions.
Keywords:
eigenfunction of Sturm-Liouville problem, nodal points of Sturm-Liouville problem, Gateaux differential, inverse Sturm-Liouville problem, inverse nodal problem, nodal points.
Received: 15.04.2013
Citation:
A. Yu. Trynin, “On inverse nodal problem for Sturm-Liouville operator”, Ufa Math. J., 5:4 (2013), 112–124
Linking options:
https://www.mathnet.ru/eng/ufa227https://doi.org/10.13108/2013-5-4-112 https://www.mathnet.ru/eng/ufa/v5/i4/p116
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Abstract page: | 547 | Russian version PDF: | 236 | English version PDF: | 34 | References: | 98 | First page: | 2 |
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