Related papers: Uniform stability for the inverse Sturm-Liouville …
The regularized trace formula of first order for the Sturm-Liouville equation with spectral parameter in the boundary conditions is obtained.
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…
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 show in a rigorous way that Crum's result on equal eigenvalue spectrum of Sturm-Liouville problems can be obtained iteratively by successive Darboux transformations. It can be shown that all neighbouring Darboux-transformed potentials of…
In this work, we use the \textit{regularized sampling method} to compute the eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval. We work out an example by computing a few eigenvalues and their…
In this paper we examine spectral properties of a family of periodic singular Sturm-Liouville problems which are highly non-self-adjoint but have purely real spectrum. The problem originated from the study of the lubrication approximation…
Denote by $L_D$ the Sturm-Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$ with Dirichlet boundary conditions $y(0)=y(\pi)=0$. Let $\{\lambda_k\}_1^\infty$ and $\{\alpha_k\}_1^\infty$ be the sequences of the eigenvalues…
In the present paper, motivated by point interaction, we propose a new and explicit approach to inverse Sturm-Liouville eigenvalue problems under Dirichlet boundary. More precisely, when a given Sturm-Liouville eigenvalue problem with the…
We continue the study of boundary data maps, that is, generalizations of spectral parameter dependent Dirichlet-to-Neumann maps for (three-coefficient) Sturm-Liouville operators on the finite interval $(a,b)$, to more general boundary…
In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…
We introduce a novel approach for dealing with eigenvalue problems of Sturm-Liouville operators generated by the differential expression \begin{equation*} Ly=\frac{1}{r}\left( -(p\left[ y^{\prime }+sy\right] )^{\prime }+sp\left[ y^{\prime…
In this study by applying an own technique we investigate some asymptotic approximation properties of new type discontinuous boundary-value problems, which consists of a Sturm-Liouville equation together with eigenparameter-dependent…
In this paper, by using the similar methods of [O. Sh. Mukhtarov and M. Kadakal, Some spectral properties of one Sturm-Liouville type problem with discontinuous weight, Siberian Mathematical Journal, 46 (2005) 681-694] we extend some…
We study the asymptotic behaviour of eigenvalues and eigenfunctions of a boundary value problem for the Sturm-Liouville operator with general boundary conditions and the weight function perturbed by the so-called $\delta'$-like sequence…
We obtain a uniform stability of recovering entire functions of a special form from their zeros. To this form, one can reduce the characteristic determinants of strongly regular differential operators and pencils of the first and the second…
The paper is concerned with the stability property under perturbation $Q\to\widetilde Q$ of different spectral characteristics of a BVP associated in $L^2([0,1];\Bbb C^2)$ with the following $2\times2$ Dirac type equation…
We consider a Sturm--Liouville $Ly=-y''+q(x)y$ in space $L_2[0,\pi]$ with potential from Sobolev space $W_2^{-1}[0,\pi]$. Moreover, we assume, that $q=u'$, where $u\in L_2[0,\pi]$. We consider Direchlet boundary conditions $y(0)=y(\pi)=0$,…
We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations…
This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…
Inverse nodal problem on Dirac operator is finding the parameters in the boundary conditions, the number m and the potential function V in the Dirac equations by using a set of nodal points of a component of two component vector…