The authors extend recent results by O. H. Hald and J. R. McLaughlin [Inverse Probl. 5, 307-347 (1989; Zbl 0667.34020)] and J. R. McLaughlin [J. Differ. Equ. 73, 354-362 (1988; Zbl 0652.34029)] on the inverse spectral problem for the Sturm-Liouville equation , subject to the boundary conditions
In particular, they show that, in case the boundary conditions or depend on the eigenparameter , the potential is uniquely determined by a dense set of nodal points of eigenfunctions.