Inverse problems for discrete Sturm–Liouville operator having Bessel-type potential

Abstract

In this paper, inverse problems are studied for Sturm–Liouville difference operators having $\frac{p^2-1/4}{m^2}$ type singularity. First, we define the Green's function and the corresponding Weyl function, some of their properties are investigated, and we give a method to find the potential function. Then we give the solution of the inverse nodal problem and present a constructive procedure for the solution of the inverse problem by using nodes.

Keywords:

• Discrete Sturm–Liouville problem
• Weyl function
• inverse problem
• nodal points
• potential function

Mathematics Subject Classifications:

• 39A06
• 39A12
• 39A70
• 34A55

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is partially supported by the University of Kashan under grant number 1222639/2.