Etibar S. Panakhov

A uniqueness theorem for inverse nodal problem

In this article, it is found that the asymptotic formulas for nodal points and nodal length for the differential operators having singularity type at the points 0 and π, it is shown that the potential function can be determined from the positions of the nodes for the eigenfunctions.

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

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 n th 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.

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

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.

Fractional Solutions of Bessel Equation with N-Method

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N ν method, we derive the fractional solutions of the equation.

Spectral problem for diffusion operator

Abstract In this paper, we study the inverse problem with two given spectra for diffusion operator on a finite interval. Making use of the Levitan’s method, we show that the kernels and are generalized degeneracy in the extended sense.

A Uniqueness Theorem for Bessel Operator from Interior Spectral Data

Inverse problem for the Bessel operator is studied. A set of values of eigenfunctions at some internal point and parts of two spectra are taken as data. Uniqueness theorems are obtained. The approach that was used in investigation of problems with partially known potential is employed.

Solution of a discontinuous inverse nodal problem on a finite interval

In this paper, the inverse problem of recovering the potential function, on a general finite interval, of a singular Sturm-Liouville problem with a new spectral parameter, called the nodal point, is studied. In addition, we give an asymptotic formula for nodal points and the density of the nodal set.

Half inverse problem for singular differential operator

A spectral analysis for the Sturm–Liouville equation defined on (0,1] and singularity of type at zero is investigated (l is an integer). As known, the potential function q(x) in the singular Sturm–Liouville problem can be uniquely determined from two spectrum. In this study, we show that if q(x) is prescribed on (1/2,1], then only one spectrum is sufficient to determine q(x) on the interval (0,1/2).

Inverse problem for a singular differential operator

In this paper, we give the solution of the inverse Sturm-Liouville problem on two partially coinciding spectra. In particular, in this case we obtain Hochstadts theorem concerning the structure of the difference q(x)-q@?(x) for the singular Sturm Liouville problem defined on the finite interval (0,@p) having the singularity type 14sin^2x at the points 0 and @p.

Half inverse problem for operators with singular potential

A half-inverse problem for Sturm-Liouville operators consists of reconstruction of this operator by its spectrum and half of the potential. In this study, we show that if q(x) is prescribed on (π/2, π), then, only one spectrum is sufficient to determine q(x) on the interval (0, π/2) for the Sturm-Liouville equation having singularity type 1/sin2 x on (0, π).