On the inverse nodal problems for discontinuous Sturm–Liouville operators

Abstract

In this paper, we discuss the inverse nodal problems for discontinuous Sturm–Liouville operators with Robin boundary conditions. We show that the potential q up to its mean value on the interval [0,1] and coefficients h, H, ba can be uniquely determined by the twin-dense nodal subset on the subinterval [a0,b0], a0<12<b0. In addition, we still establish several uniqueness theorems by the left twin-dense nodal subset on the interval [a0,12] and additional information, respectively.