Inverse Nodal Problems for Dirac Type Integro Differential System with a Nonlocal Boundary Condition

TL;DR

This paper studies inverse nodal problems for a Dirac-type integro-differential system with nonlocal boundary conditions, providing asymptotic formulas, uniqueness results, and a solution procedure.

Contribution

It introduces a novel inverse nodal problem framework for Dirac-type integro-differential systems with nonlocal boundary conditions, including uniqueness and solution methods.

Findings

Asymptotic formulas for solutions, eigenvalues, and nodal points.

Uniqueness of boundary parameter and potential function from dense nodal data.

An effective procedure for solving the inverse nodal problem.

Abstract

In this work, the Dirac-type integro di{\S}erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal points. We also investigate the inverse nodal problem and prove that given a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered di{\S}erential system. We also provide an e{\S}ective procedure for solving the inverse nodal problem.