Abstract
An inverse problem for the Sturm-Liouville equation with a potential depending on the spectral parameter is considered. It is proved that the spectra of the corresponding Dirichlet problems on [0, b] and [b, a] and that of the Dirichlet-Neumann problem on [0, a] (a > b) uniquely determine the potential almost everywhere. These problems arise when one considers small vibrations of a smooth inhomogeneous partially damped string clamped at an inner point.
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Pivovarchik, V. (1999). A Particular Case of The Inverse Problem for The Sturm-Liouville Equation with Parameter-Dependent Potential. In: Dittrich, J., Exner, P., Tater, M. (eds) Mathematical Results in Quantum Mechanics. Operator Theory Advances and Applications, vol 108. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8745-8_32
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DOI: https://doi.org/10.1007/978-3-0348-8745-8_32
Publisher Name: Birkhäuser, Basel
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