On inverse nodal problem for Sturm-Liouville operator

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.