On the main equation of inverse sturm-liouville operator with discontinuous coefficient

TL;DR

This paper investigates a boundary value problem for a Sturm-Liouville operator with a discontinuous coefficient, deriving a main equation crucial for solving the inverse problem and establishing the uniqueness of its solution.

Contribution

It introduces a main equation for inverse Sturm-Liouville problems with discontinuous coefficients and proves the uniqueness of solutions.

Findings

Main equation for inverse problem derived

Uniqueness of solution proved

Applicable to Sturm-Liouville operators with discontinuities

Abstract

In this work, a boundary value problem for Sturm-Liouville operator with discontinuous coefficient is examined. The main equation is obtained which has an important role in solution of inverse problem for boundary value problem and uniqueness of its solution is proved. Uniqueness theorem for the solution of the inverse problem is given.