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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 {\it O. H. Hald} and {\it J. R. McLaughlin} [Inverse Probl. 5, 307-347 (1989; Zbl 0667.34020)] and {\it 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 of ODE 34B24 Sturm-Liouville theory
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