UNIQUENESS THEOREMS FOR STURM-LIOUVILLE OPERATORS WITH INTERIOR TWIN-DENSE NODAL SET

Yu Wang
2017 Electronic Journal of Differential Equations   unpublished
We study Inverse problems for the Sturm-Liouville operator with Robin boundary conditions. We establish two uniqueness theorems from the twin-dense nodal subset W S ([ 1−ε 2 , 1 2 ]), 0 < ε ≤ 1, together with parts of either one spectrum, or the minimal nodal subset {x 1 n } ∞ n=1 on the interval [0, 1 2 ]. In particular, if one spectrum is given a priori, then the potential q on the whole interval [0, 1] can be uniquely determined by W S ([ 1−ε 2 , 1 2 ]) for any S and arbitrarily small ε.
fatcat:eng4tbtyizc45eifqa337xzsqi