‎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 ...

‎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 ...

where λ is a spectral parameter, Y (x) = [yk(x)]k=1,d is a column vector, Q(x) and M(x, t) are d×d real symmetric matrix-valued functions, and h and H are d×d real symmetric constant matrices. M(x, t) is an integrable function on the set D0 def ={(x, t) : 0≤ t ≤ x ≤ π, x, t ∈ R}, Q ∈ C1[0,π], where C1[0,π] denotes a set whose element is a continuously differentiable function on [0,π]. In partic...

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...

The so-called Ambarzumyan theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator − d2 dx2 +q with an integrable real-valued potential q on [0,π] are {n2 : n 0} , then q = 0 for almost all x ∈ [0,π] . In this work, the classical Ambarzumyan theorem is extended to star graphs with Dirac operators on its edges. We prove that if the spectrum of Dirac operator on star graphs ...

We consider a Sturm–Liouville operator with an integrable potential q on the unit interval I = [ 0 , 1 ] . Schrödinger real compactly supported half line and line, where this coincides vanishes outside I. determine relationships between eigenvalues of such operators obtain estimates in terms potentials.

We show how a number of NP-complete as well as NP-hard problems can be reduced to the Sturm-Liouville eigenvalue problem in the quantum setting with queries. We consider power queries which are derived from the propagator of a system evolving with a Hamiltonian obtained from the discretization of the Sturm-Liouville operator. We use results of our earlier paper concering the complexity of the S...

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.

Consider the minimal Sturm-Liouville operator A = Amin generated by the differential expression