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


Adiloglu A., GÜRDAL M., KINCI A. N.

ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, vol.89, no.4, pp.2547-2561, 2017 (Peer-Reviewed Journal) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 89 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1590/0001-3765201720160075
  • Journal Name: ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.2547-2561
  • Keywords: Asymptotic formulas for eigenvalues, boundary value problems, inverse problems, spectral analysis of ordinary differential operators, Sturm-Liouville theory, transformation operator, EIGENVALUE PROBLEMS, SINGULAR POTENTIALS, SPECTRAL PROBLEMS, OPERATORS, INTERVAL

Abstract

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.