Inverse nodal problems for Sturm-Liouville equation with nonlocal boundary conditions

TL;DR

This paper investigates inverse nodal problems for Sturm-Liouville equations with nonlocal boundary conditions, demonstrating unique coefficient determination and providing an algorithm for reconstructing the potential and boundary coefficients.

Contribution

It introduces a method to uniquely recover coefficients in Sturm-Liouville problems with nonlocal boundary conditions using nodal data and offers a reconstruction algorithm.

Findings

Coefficients can be uniquely determined from dense nodal points.

An explicit algorithm for potential and boundary coefficient reconstruction is provided.

The study extends inverse problem techniques to nonlocal boundary conditions.

Abstract

In this paper, a Sturm--Liouville problem with some nonlocal boundary conditions of the Bitsadze-Samarskii type is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we give an algorithm for the reconstruction of the potential function and some other coefficients in the boundary conditions.