Related papers: On Sturm-Liouville Equations with Several Spectral…
Classical Sturm-Liouville problems of $q$-difference variables are extended for symmetric discrete functions such that the corresponding solutions preserve the orthogonality property. Some illustrative examples are given in this sense.
This paper studies a Sturm--Liouville boundary value problem in which one of the boundary conditions depends bilinearly on the spectral parameter. The differential equation is considered on the interval $(0,1)$ with a classical boundary…
The spectral analysis of the Sturm-Liouville operator defined on a finite segment is the subject of an extensive literature. Sturm-Liouville operators on a finite segment are well studied and have numerous applications. The study of such…
In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymptotic iteration method we find a degree independent…
We consider the spectral problem generated by the Sturm-Liouville equation with an arbitrary complex-valued potential q(x) and irregular boundary conditions. We establish necessary and sufficient conditions for a set of complex numbers to…
In this work, we consider not only a discontinuous boundary-value problem with retarded argument and four supplementary transmission conditions at the two points of discontinuities but also, eigenparameter-dependent boundary conditions and…
We study a second-order differential equation involving a quasi-derivative, leading to a non-self-adjoint Sturm--Liouville-type problem with four coefficient functions. To analyze this equation, we develop a generalized Pr\"ufer…
The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…
This paper deals with the inverse spectral problem for a non-self-adjoint Sturm-Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential $q$ is known a priori on a subinterval $ \left[ b,\pi…
Recently, there appeared a significant interest in inverse spectral problems for non-local operators arising in numerous applications. In the present work, we consider the operator with frozen argument $ly = -y''(x) + p(x)y(x) + q(x)y(a),$…
In this paper, we study spectral problems for the Sturm-Liouville operator with arbitrary complexvalued potential q(x) and two-point boundary conditions. All types of mentioned boundary conditions are considered. We ivestigate in detail the…
This paper deals with the computation of the eigenvalues of two-parameter Sturm- Liouville (SL) problems using the Regularized Sampling Method, a method which has been effective in computing the eigenvalues of broad classes of SL problems…
A spectral parameter power series (SPPS) representation for regular solutions of singular Bessel type Sturm-Liouville equations with complex coefficients is obtained as well as an SPPS representation for the (entire) characteristic function…
The regularized trace formula of first order for the Sturm-Liouville equation with spectral parameter in the boundary conditions is obtained.
We study spectral properties of energy-dependent Sturm-Liouville equations, introduce the notion of norming constants and establish their interrelation with the spectra. One of the main tools is the linearization of the problem in a…
The spectrum of the singular indefinite Sturm-Liouville operator $$A=\text{\rm sgn}(\cdot)\bigl(-\tfrac{d^2}{dx^2}+q\bigr)$$ with a real potential $q\in L^1(\mathbb R)$ covers the whole real line and, in addition, non-real eigenvalues may…
We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral…
We consider two closely related Riccati equations of constant parameters whose particular solutions are used to construct the corresponding class of supersymmetrically-coupled second-order differential equations. We solve analytically these…
In this study, a formula for regularized sums of eigenvalues of a Sturm-Liouville problem with retarded argument at the point of discontinuity is obtained. Moreover, oscillation properties of the related problem is investigated.
This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and…