On the quasinodal map for the diffusion operator

We study inverse nodal problems for the diffusion operator with separated boundary conditions. It is shown that the space of diffusion operators characterized by B:=B(p,q,α,β), where (p,q,α,β)∈W11(0,π)×L1(0,π)×[0,π)2, under a certain metric, is homeomorphic (i.e., continuous, open bijection between two topological spaces) to the partition set of the space of quasinodal sequences. As a consequence, the inverse nodal problem defined on the partition set of admissible sequence, is stable.