Related papers: On some class of singular Sturm-Liouville problems
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local…
In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas…
We prove the existence of solutions to the Sturm-Liouville (SL) equation -y"(x)+q(x)y(x) = s^2 y(x) with periodic and quasi-periodic potential q(x) using theory of SL vessels, implementing a Backlund transformation of SL equation. In this…
In this paper, the Sturm-Liouville problem with nonseparated quasiperiodic boundary conditions is considered. We study the recovery of the problem parameters from the Hill-type discriminant, the Dirichlet spectrum, and the sequence of…
This paper deals with the Sturm-Liouville problem with singular potential of the Sobolev space $W_2^{-1}$ and polynomials of the spectral parameter in a boundary condition. We prove the uniform boundedness and the uniform stability for the…
Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the…
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…
The limit distribution of the discrete spectrum of the Sturm-Liouville problem with complex-valued polynomial potential on an interval, on a half-axis, and on the entire axis is studied. It is shown that at large parameter values, the…
We study the Sturm--Liouville operator $$ T(\varepsilon)y=-\frac{1}{\varepsilon}y''+ p(x)y, $$ with concrete $\mathcal{PT}$-- symmetric potential $p(x) = ix$ and Dirichlet boundary conditions on the segment $[-1,1]$. Here $\varepsilon \in…
We obtain the uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L_{t}(q) with a potential q\inL_{1}[0,1] and with t-periodic boundary conditions, t\in(-{\pi},{\pi}]. Using these formulas, we…
We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete…
It is constructively proved that for class $A_{r,\gamma}=\{q\in L_{1,loc}(0,1): q\leq 0, \int_0^1 rq^\gamma\,dx\leqslant 1\}$, where $r\in C[0,1]$ is uniformly positive weight and $\gamma>1$, there exists a unique potential $\hat q\in…
We revisit basics of classical Sturm-Liouville theory and, as an application, recover Bochner's classification of second order ODEs with polynomial coefficients and polynomial solutions by a new argument. We also outline how a wider class…
In this article, we first introduce a singular fractional Sturm-Liouville eigen-problems (SFSLP) on unbounded domain. The associated fractional differential operators in these problems are both Weyl and Caputo type . The properties of…
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…
In recent years, there appeared a considerable interest in the inverse spectral theory for functional-differential operators with constant delay. In particular, it is well known that specification of the spectra of two operators $\ell_j,$…
For the equations $y''=P(x,y) + 3Q(x,y)y' + 3R(x,y){y'}^2 + S(x,y){y'}^3$ the problem of equivalence is considered. Some classical results are resumed in order to prepare the background for the study of special subclass of such equations,…
In this paper, we consider a wave equation on a bounded domain with a Sturm-Liouville operator with a singular intermediate coefficient and a singular potential. To obtain and evaluate the solution, the method of separation of variables is…
We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the…