A Partial Inverse Problem for the Sturm-Liouville Operator with Constant Delays on a Star Graph

In this work we consider boundary value problems for the Sturm-Liouville operator with constant delays on a star graph. We assume that the potentials and the delay constants are known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential and the the delay constant on remaining edge from the part of the spectrum. The uniqueness of the solution of the inverse problem is proved. A constructive method is developed for the solution of the inverse problem.