Traces and inverse nodal problems for a class of Sturm-Liouville operators with retarded argument

TL;DR

This paper explores inverse nodal problems and traces for a class of discontinuous Sturm-Liouville operators with retarded arguments, providing new insights into their spectral properties and solution reconstruction methods.

Contribution

It introduces novel techniques for solving inverse nodal problems for discontinuous Sturm-Liouville operators with retarded arguments and transmission conditions.

Findings

Derived trace formulas for the operators.

Established uniqueness results for inverse problems.

Developed reconstruction algorithms for potential functions.

Abstract

In this study, we investigate the traces and solutions of inverse nodal problems of discontinuous Sturm-Liouville operators with retarded argument and with a finite number of transmission conditions.