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Anais da Academia Brasileira de Ciências

Print version ISSN 0001-3765On-line version ISSN 1678-2690

Abstract

ADILOGLU, ANAR; GURDAL, MEHMET  and  KINCI, AYŞE N.. Uniqueness Properties of The Solution of The Inverse Problem for The Sturm-Liouville Equation With Discontinuous Leading Coefficient. An. Acad. Bras. Ciênc. [online]. 2017, vol.89, n.4, pp.2547-2561. ISSN 0001-3765.  https://doi.org/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.

Keywords : Asymptotic formulas for eigenvalues; boundary value problems; inverse problems; spectral; analysis of ordinary differential operators; Sturm-Liouville theory; transformation operator.

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