Inverse nodal problems for the Sturm–Liouville operator with a constant delay

Abstract

We study inverse nodal problems for non-self-adjoint second-order differential operator with a constant delay. The uniqueness theorem is proved for this inverse problem and a constructive procedure for the solution of the inverse nodal problems is provided. We show that the space of delay differential operators characterized by (q,α,β)∈L1(a,π)×[0,π)2, a∈(0,π), under a certain metric, is homeomorphic to the partition set of the space of quasinodal sequences, which is all admissible sequences X={Xnj}n≥2,j=1,n−1¯ which form sequences that converge to q, α and β individually. As a consequence, the inverse nodal problem, when defined on the partition set of admissible sequence induced by the same equivalence relation, is stable.