We give a comprehensive treatment of Sturm–Liouville operators whose coefficients are measures including a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl–Titchmarsh–Kodaira theory. We avoid previous technical restrictions and, at the same time, extend all results to a larger class of operators. Our operators include classical Sturm– Liouville operators,...

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

In this article we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter l. This nonlinear dependence on l is allowed both in the leading coefficient and in the potential. We extend the traditional notions of eigenvalues and eigenfunctions to this more general setting. Our main result generalizes the re...

In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.

Following earlier work on fourth order problems, we develop a shooting method to approximate the eigenvalues of 6th order Sturm-Liouville problems using a spectral function N() which counts the number of eigenvalues less than. This requires anòscillation' count obtained from certain solutions of the diierential equation, and we develop explicit algorithms for obtaining the exact oscillation cou...

In this paper, we study the inverse problem for Sturm Liouville with conformable fractional differential operators of order and finite number interior discontinuous conditions. For aim first, asymptotic formulas solutions, eigenvalues eigenfunctions are calculated. Then some uniqueness theorems proposed eigenvalue proved. Finally, Hald's theorem 
 Sturm-Liouville is developed.

where the potentials are given functions. Under various boundary conditions, Sturm and Liouville established that solutions of problem (1) can exist only for particular values of the real parameter λ, which is called an eigenvalue. Relevant examples of linear Sturm-Liouville problems are the Bessel equation and the Legendre equation. The classical Sturm-Liouville theory does not depend upon the...

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– ...

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...