Inverse nodal problems on quantum tree graphs

We consider inverse nodal problems for the Sturm–Liouville operators on the tree graphs. Can only dense nodes distinguish the tree graphs? In this paper it is shown that the data of dense-nodes uniquely determines the potential (up to a constant) on the tree graphs. This provides interesting results for an open question implied in the paper.

Inverse nodal problems for integro-differential operators with a constant delay

We study inverse nodal problems for Sturm–Liouville operator perturbed by a Volterra integral operator with a constant delay. We have estimated nodal points and nodal lengths for this operator. Moreover, by using these data, we have shown that the potential function of this operator can be established uniquely.