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Inverse nodal problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions. (English) Zbl 0860.34007

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 \(-y''+q(x) y=\lambda y\), subject to the boundary conditions \[ (*)\quad y'(0)= hy(0),\;y'(1)=-H(y)(1) \quad\text{or}\quad (**)\quad y(0)= y(1)=0. \] In particular, they show that, in case the boundary conditions \((*)\) or \((**)\) depend on the eigenparameter \(\lambda\), the potential \(q\) is uniquely determined by a dense set of nodal points of eigenfunctions.

MSC:

34A55 Inverse problems involving ordinary differential equations
34B24 Sturm-Liouville theory
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