In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.

The equation of motion a microparticle in various force fields is the Schr¨odinger wave equation.Many questions quantum mechanics, particular thermal radiation electromagneticwaves, lead to problem separability singular differential operators. One such operator isthe above Schr?dinger operator. In this paper, named studied by methods offunctional analysis. Found sufficient conditions for existe...

In this study, fractional differential transform method (FDTM), which is a semi analytical-numerical technique, is used for computing the eigenelements of the Sturm-Liouville problems of fractional order. The fractional derivatives are described in the Caputo sense. Three problems are solved by the present method. The calculated results are compared closely with the results obtained by some exi...

In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.

Abstract We consider discrete Sturm–Liouville-type equations of the form $$\begin{aligned} \varDelta (r_n\varDelta x_n)=a_nf(x_{\sigma (n)})+b_n. \end{aligned}$$ ? ( r n x )</mml:...

This paper deals with a class of nonlinear fractional Sturm–Liouville boundary value problems. Each sub equation in the system is partial including second kinds Fredholm integral and p-Laplacian operator, simultaneously. Infinitely many solutions are derived due to perfect involvements calculus theory variational methods some simpler more easily verified assumptions.

We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and −K are extrema of the eigencurves of this family. This characterization mak...

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 &#x0D; Sturm-Liouville is developed.

We derive Povzner–Wienholtz-type self-adjointness results form× m matrix-valued Sturm–Liouville operators T = R [

In this paper, we construct the new integral representation of Jost solution Sturm-Liouville equation with impuls in semi axis $[0,+\infty )$ and give type relation, examine properties Kernel function their partial derivatives $x$ $\ t$, constructed obtain differential provided by function. Finally, paper prove uniqueness determination potential scattering data.