Inverse nodal problem for a class of nonlocal sturm‐liouville operator

Abstract

Inverse nodal problem consists in constructing operators from the given nodes (zeros) of their eigenfunctions. In this work, the Sturm‐Liouville problem with one classical boundary condition and another nonlocal integral boundary condition is considered. We prove that a dense subset of nodal points uniquely determine the boundary condition parameter and the potential function of the Sturm‐Liouville equation. We also provide a constructive procedure for the solution of the inverse nodal problem.

Keywords:

• Sturm‐Liouville problem
• nonlocal integral condition
• inverse nodal problem
• potential function
• reconstruction formula