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.
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