Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions

TL;DR

This paper investigates inverse spectral problems for Sturm-Liouville equations with a spectral parameter linearly in a boundary condition, providing conditions for solving these problems from eigenvalues, norming constants, or two spectra.

Contribution

It introduces necessary and sufficient conditions for solving inverse Sturm-Liouville problems with spectral parameters in boundary conditions, expanding the theoretical understanding of these inverse problems.

Findings

Derived necessary and sufficient conditions for inverse problems

Solved inverse problems from eigenvalues and norming constants

Addressed inverse problems from two spectra

Abstract

Inverse problems of recovering the coefficients of Sturm-Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.