Inverse problems for Sturm-Liouville difference equations

Abstract

We consider a discrete Sturm-Liouville problem with Dirichlet boundary conditions. We show that the specification of the eigenvalues and weight numbers uniquely determines the potential. Moreover, we also show that if the potential is symmetric, then it is uniquely determined by the specification of the eigenvalues. These are discrete versions of well-known results for corresponding differential equations.

Inverse Problems for Difference Equations with Quadratic Eigenparameter Dependent Boundary Conditions-II

“…Given the weights and the eigenvalues for the above boundary value problem with 1 s ≤ and 1 p ≤ , a unique reconstruction of the potential was obtained, see [1] for details. This can be considered as a generalization of the results obtained in [4] in that more general boundary conditions are considered.…”

“…A comprehensive introduction to difference equations can be found, for example, in [2] and [3], amongst others. In particular, inverse problems for Sturm-Liouville difference equations with Dirichlet boundary conditions have been considered recently by Bohner and Koyunbakan in [4] where they show that the specification of the eigenvalues and weights uniquely determines the potential. In addition, they also prove that if the potential is symmetric, then it is uniquely determined by the eigenvalues only-this result can also be found in [5] where it is proved using different methods.…”

A Uniqueness Theorem on Inverse Spectral Problems for the Sturm–Liouville Differential Operators on Time Scales

“…N = 0, we have a difference operator. Inverse spectral problems for the difference operators were studied in [11][12][13][14][15] and other works. In [11] the coefficients of finite discrete Sturm-Liouville type bondary value problem are recovered from the spectrum and the set of normalization constants or from two spectra.…”

A certain class of surfaces on product time scales with interpretations from economics

“…So, it has various applications involving non-continuous domains like modeling of certain bug populations, chemical reactions, phytoremediation of metals, wound healing, maximization problems in economics and traffic problems. In recent years, several authors have obtained many important results about different topics on time scales (see [1], [12], [13], [21], [23], [24], [27], [28], [30], [41]).…”