Inverse Sturm-Liouville problem with singular potential and spectral parameter in the boundary conditions

2024/09/03 by Egor E. Chitorkin, Chitorkin, E. E., N. P. Bondarenko +1 · 1 citation
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2409.02254

openalex publication_date 2024/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse spectral problem that consists in the recovery of the potential and the polynomials from some part of the spectrum. We for the first time prove local solvability and stability for this type of inverse problems. Furthermore, the necessary and sufficient conditions on the given subspectrum for the uniqueness of solution are found, and a reconstruction procedure is developed. Our main results can be applied to a variety of partial inverse problems. This is illustrated by an example of the Hochstadt-Lieberman-type problem with polynomial dependence on the spectral parameter in the both boundary conditions.

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