Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a SturmLiouville d...

In this study by modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we investigate some spectral properties of one Sturm-Liouville type problem on two disjoint intervals.

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigen-parameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.

The zeros of the eigenfunctions of self-adjoint Sturm–Liouville eigenvalue problems interlace. For these problems interlacing is crucial for completeness. For the complex Sturm–Liouville problem associated with the Schrödinger equation for a non-Hermitian PT-symmetric Hamiltonian, completeness and interlacing of zeros have never been examined. This paper reports a numerical study of the Sturm– ...

this paper deals with the boundary value problem involving the differential equationbegin{equation*}    ell y:=-y''+qy=lambda y, end{equation*} subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$ begin{equation*}    y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0),end{equation*}where $q(x),  a_1 , a_2$ are  real, $qin l...

An inverse spectral problem is studied for the non-selfadjoint matrix Sturm–Liouville differential equation on the half-line. We give a formulation of the inverse problem, prove the corresponding uniqueness theorem and provide a constructive procedure for the solution of the inverse problem by the method of spectral mappings. The obtained results are natural generalizations of the classical res...

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 Hochstadt's theorem concerning the structure of the difference q(x) − ˜ q(x) for the singular Sturm Liouville problem defined on the finite interval (0, π) having the singularity type 1 4 sin 2 x at the points 0 and π.

This paper is concerned with the construction and study of specific finite and infinite integral transforms arising from a singular Sturm-Liouville problem on a half line, which is connected to the hydrogen atom equation. The paper goes further to describe fully the image of some spaces of square integrable functions with respect to some measure under the finite and infinite integral transforms...

‎this paper deals with the singular sturm-liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of sturm-liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...