Inverse Spectral and Inverse Nodal Problems for Energy-Dependent Sturm-Liouville Equations with Δ-Interaction (original) (raw)
Related papers
Inverse spectral problems for energy-dependent Sturm–Liouville equations
2012
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 description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.
Inverse Problems in Science and Engineering
Inverse nodal problems for the Sturm–Liouville equation in a finite interval with boundary conditions depending polynomially on the spectral parameter are studied. We prove a uniqueness theorem: nodal points uniquely determine the polynomials of the boundary conditions and the potential function of the Sturm–Liouville equation. For these inverse nodal problems we provide constructive procedures.
The inverse nodal problem for a differential operator with an eigenvalue in the boundary condition
Applied Mathematics Letters, 2008
We consider the Sturm-Liouville problem with an eigenvalue dependent boundary condition. In this work, by using method of Yang [X.F. Yang, A solution of the inverse nodal problem, Inverse Problems 13 (1997) 203-213.], we reconstruct the potential of the Sturm-Liouville problem with an eigenvalue in the boundary condition from nodal points (zeros of eigenfunctions). Also, we give a uniqueness theorem.
2018
In this article, we extend solution of inverse nodal problem for one-dimensional p-Laplacian equation to the case when the boundary condition is polynomially eigenparameter. To find the spectral data as eigenvalues and nodal parameters, a Prüfer substitution is used. Then, we give a reconstruction formula of the potential function by using nodal lengths. This method is similar to used in [24], and our results are more general.
In this manuscript, we study the inverse problem for non self-adjoint Sturm–Liouville operator −D 2 + q with eigenpa-rameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining a new Hilbert space and using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at some interior point and parts of two sets of eigenvalues.
Inverse spectral problem for the Sturm Liouville equation
Inverse Problems, 2003
This paper discusses a new numerical approach to computing the potential q in the Sturm-Liouville problem −y + qy = λy on a compact interval. It is shown that an algorithm to recover q from eigenvalues and multiplier constants can be derived. Examples of some test problems, and questions of efficiency are discussed.