Uniqueness Properties of The Solution of The Inverse Problem for The Sturm-Liouville Equation With Discontinuous Leading Coefficient

An Acad Bras Cienc. Oct-Dec 2017;89(4):2547-2561. doi: 10.1590/0001-3765201720160075.


The present paper studies uniqueness properties of the solution of the inverse problem for the Sturm-Liouville equation with discontinuous leading coefficient and the separated boundary conditions. It is proved that the considered boundary-value is uniquely reconstructed, i.e. the potential function of the equation and the constants in the boundary conditions are uniquely determined by given Weyl function or by the given spectral data.