On a uniqueness theorem of Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter

Abstract

Inverse nodal problems for Sturm-Liouville equations associated with boundary conditions polynomially dependent on the spectral parameter are studied. The authors show that a twin-dense subset W B ([a, b]) can uniquely determine the operator up to a constant translation of eigenparameter and potential, where [a, b] is an arbitrary interval which contains the middle point of the domain of the operator and B is a subset of N which satisfies some condition (see Theorem 4.2).

Uniqueness of the potential in conformable Sturm‐Liouville problem

“…Compared to the direct problem, the inverse SLP is both attractive and open to improvement [24, 25]. In the inverse problem, parameters such as spectrum, norming constants, zeros of eigenfunctions, and Weyl function are given, and the coefficient of the equation $$$ q(x) $$$, the potential $$$ q $$$, and the coefficients in the boundary conditions are found [26–29]. Normally, two spectra or a spectrum and norming constants are sufficient to find the potential $$$ q $$$ as uniquely.…”