Inverse nodal problems of discontinuous Sturm–Liouville operator

Abstract

We study inverse nodal problems for the second-order differential operator with discontinuity inside a finite interval. In particular, we solve the uniqueness, reconstruction and stability problems using the nodal set of its eigenfunctions. Furthermore, we show that the space of discontinuous Sturm–Liouville operators characterized by B=(q,h,H,a1,a2)∈L1(0,1)×R4 such that ∫01q(x)dx=0 is homeomorphic to the partition set of the space of quasinodal sequences, which are all admissible sequences X={Xnj}n⩾2,j=1,n−1¯ which form sequences that converge to q, h, H, and 2a2a1+a1−1 individually.