Firat University, Department of Mathematics, 23119, Elazig, Turkey.
*Permanent address: Institute of Mathematics and Mechanics, Azerbaijan Academy of Sciences, 370143, Baku, Azerbaijan. E-mail: epenahov@hotmail.com, hkoyunbakan@gmail.com
AMS subject classification: 34B24, 34B99.
The inverse nodal problem for the Sturm–Liouville operator is the problem of finding the potential function q and the boundary conditions using the nodal points. The purpose of this paper is to present a method for solving the inverse nodal problem for a singular differential operator on a finite interval. We find asymptotic formulas for nodal points and the nodal lengths for differential operators having singularity type at the point 0. We also determine the potential function from the position of nodes.
Singular differential equation, eigenfunction, nodal point
