In the paper, we study problem of recovering Sturm--Liouville operator with frozen argument from its spectrum and additional data. For this inverse problem, establish a substantial property uniform stability, which consists in that potential depends Lipschitz continuously on input

In this paper, we consider the inverse problem for Sturm-Liouville operators with eigenparameter dependent boundary conditions on time scales. We give new uniqueness theorems and investigate its some special cases.

in this paper we apply the homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of sturm-liouville type on $[0,pi]$ with neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued sign-indefinite number of $c^{1}[0,pi]$ and $lambda$ is a real parameter.

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

In this work, we have estimated nodal points and nodal lengths for the diffusion operator. Furthermore, by using these new spectral parameters, we have shown that the potential function of the diffusion operator can be established uniquely. An analogous inverse problem was solved for the Sturm–Liouville problem in recent years. c © 2005 Elsevier Ltd. All rights reserved.

In this paper the inverse eigenvalue problem of recovering the real coefficients in a Sturm–Liouville problem with nonselfadjoint boundary conditions depending on the spectral parameter from the eigenvalues is solved using entire-function theory and the solution of a Marchenko integral equation.

In this paper, the inverse problem of recovering the potential function, on a general finite interval, of a singular Sturm–Liouville problem with a new spectral parameter, called the nodal point, is studied. In addition, we give an asymptotic formula for nodal points and the density of the nodal set. c © 2006 Elsevier Ltd. All rights reserved.

Abstract We prove local solvability and stability of the inverse Robin–Regge problem in general case, taking eigenvalue multiplicities into account. develop new approach based on reduction this to recovery Sturm–Liouville potential from Cauchy data

We show how a number of NP-complete as well as NP-hard problems can be reduced to the Sturm-Liouville eigenvalue problem in the quantum setting with queries. We consider power queries which are derived from the propagator of a system evolving with a Hamiltonian obtained from the discretization of the Sturm-Liouville operator. We use results of our earlier paper concering the complexity of the S...

We discuss direct and inverse spectral theory of self-adjoint Sturm– Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl–Titchmarsh theory for these relations. Consequently, we apply de Branges’ subspace ordering theorem to obtain inverse uniqueness results for the associated spectral measure. The results can be applied to...