Solving inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko– Faddeev theorem (in the continuous case) [6] and the Guseinov theorem (in the discrete case) [4], guarantees the uniqueness of solution of the...

When solving the inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential, one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko–Faddeev theorem [8] (in the continuous case, for the discrete case see [4, 6]), guarantees the uniqueness of the solution of the inve...

in this paper, inverse laplace transform method is applied to analytical solution of the fractional sturm-liouville problems. the method introduces a powerful tool for solving the eigenvalues of the fractional sturm-liouville problems. the results  how that the simplicity and efficiency of this method.

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.

We develop an analog of classical oscillation theory for Sturm– Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type ...

In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem second-order differential equation containing fractional derivative operator. The differentiation operator was considered according to two definitions: Gerasimov-Caputo Riemann-Liouville-Visualizations eigenfunctions, biorthogonal system, distribution on real axis were present...

We establish the connection between Sturm–Liouville equations on time scales and Sturm–Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm–Liouville equations on time scales which have been obtained by various authors in the past.

We provide a complete spectral characterization of the double commutation method for general Sturm-Liouville operators which inserts any finite number of prescribed eigenvalues into spectral gaps of a given background operator. Moreover, we explicitly determine the transformation operator which links the background operator to its doubly commuted version (resulting in extensions and considerabl...

Given the Sturm-Liouville eigenfunction expansion of an ¿2 function fix), summability theory provides means for recovering the value of fix¿) at points x0 where / is sufficiently regular. If the coefficients in the expansion are perturbed slightly (in the I^ norm), a stable summation method will recover from the perturbed expansion a good approximation to fix¿). In this paper we develop stable ...

This paper presents a method of numerically computing zeros of an analytic function for the specific application of computing eigenvalues of the Sturm-Liouville problem. The Sturm-Liouville problem is an infinite dimensional eigenvalue problem that often arises in solving partial differential equations, including the heat and wave equations. To compute eigenvalues of the Sturm-Liouville problem...