Related papers: Inverse Sturm-Liouville problems with fixed bounda…
In this paper, we investigate the sampling analysis associated with discontinuous Sturm-Liouville problem which has transmission conditions at two points of discontinuity also contains an eigenparameter in a boundary condition and two…
In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm-Liouville problem that consists in the recovery of the potential and the parameters of…
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…
We consider Sturm-Liouville operators $-y''+v(x)y$ on $[0,1]$ with Dirichlet boundary conditions $y(0)=y(1)=0$. For any $1\le p<\infty$, we give a short proof of the characterization theorem for the spectral data corresponding to $v\in…
We consider an inverse optimization spectral problem for the Sturm-Liouville operator $$\mathcal{L}[q] u:=-u''+q(x)u$$ subject to the separated boundary conditions. In the main result, we prove that this problem is related to the existence…
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…
In this paper, the inverse Sturm-Liouville problem with distribution potential and with polynomials of the spectral parameter in one of the boundary conditions is considered. We for the first time prove local solvability and stability of…
A connection, which shows the dependence of norming constants on boundary conditions, was found using the Gelfand-Levitan method for the solution of inverse Sturm-Liouville problem.
The self-adjoint matrix Sturm-Liouville operator on a finite interval with a boundary condition in the general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered operator. These…
In this paper, we for the first time prove local solvability and stability of the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The proof…
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…
In this paper, a Sturm--Liouville problem with some nonlocal boundary conditions of the Bitsadze-Samarskii type is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we…
Consider the operator $H\p=-\p''+q\p=\l\p$, $\p(0)=0$, $\p'(1)+b\p(1)=0$ acting in $L^2(0,1)$, where $q\in L^2(0,1)$ is a real potential. Let $\l_n(q,b)$, $n\ge 0$, be the eigenvalues of $H$ and $\n_n(q,b)$ be the so-called norming…
We consider the Sturm-Liouville operator Lu=u''-q(x)u with regular but not strongly regular boundary conditions. Under some supplementary assumptions we prove that the set of potentials q(x) that ensure an asymptotically multiple spectrum…
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…
Inverse spectral problems for Sturm-Liouville operators on a finite interval with non-separated boundary conditions are studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We…
The matrix Sturm-Liouville operator on a finite interval with the boundary conditions in the general self-adjoint form and with the singular potential from the class $W_2^{-1}$ is studied. This operator generalizes Sturm-Liouville operators…
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…
The inverse scattering problem is studied for the matrix Sturm-Liouville equation on the line. Necessary and sufficient conditions for the scattering data are obtained.
The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…