Reconstruction formula for the potential function of Sturm–Liouville problem with eigenparameter boundary condition

Abstract

It is known that the uniqueness of potential function of the Sturm–Liouville problem can be shown from the nodal points. In this article, we solve the inverse nodal problem of the reconstruction of the potential function q from the nodal data by a pointwise limit. We show that this convergence is in the L¹. It is mentioned that this method is based on the works of Law and Yang, but we have applied the method for the Sturm–Liouville problem depending on eigenparameter boundary conditions.

Keywords:

• Sturm–Liouville problem
• nodal points
• reconstruction formula

AMS Subject Classifications::

• 34B24
• 34A55

Acknowledgements

This work was supported in part by the Firat University, Scientific Research Project Unit under grant number: 1540.