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Reconstruction of potential function for Sturm-Liouville operator with Coulomb potential

Etibar S Panakhov1 and Murat Sat2*

Author Affiliations

1 Department of Mathematics, Firat University, Elazig, 23119, Turkey

2 Department of Mathematics, Erzincan University, Erzincan, 24100, Turkey

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Boundary Value Problems 2013, 2013:49  doi:10.1186/1687-2770-2013-49

Published: 8 March 2013


In this paper, we are concerned with an inverse problem for the Sturm-Liouville operator with Coulomb potential using a new kind of spectral data that is known as nodal points. We give a reconstruction of q as a limit of a sequence of functions whose nth term is dependent only on eigenvalue and its associated nodal data. It is mentioned that this method is based on the works of Law and Yang, but we have applied the method to the singular Sturm-Liouville problem.

MSC: 34L05, 45C05.

Coulomb potential; nodal point; reconstruction formula