Abstract
In this paper we investigate two boundary value problems on the finite interval with potentials that may have non-integrable singularity at the origin. The first problem allows unique determination of the potential by only one spectrum for certain values of the parameter in one of the boundary conditions. The second problem deals with the Dirichlet problem for potentials which are the sum of Bessel's main part with constant bounded from below and non-integrable potential. Uniqueness results are proved for both problems.
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