INVERSE PROBLEMS FOR THE STURM-LIOUVILLE EQUATION WITH THE DISCONTINUOUS COEFFICIENT


Nabiev A. A. , GÜRDAL M. , SALTAN S.

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, vol.7, no.2, pp.559-580, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.11948/2017035
  • Title of Journal : JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
  • Page Numbers: pp.559-580
  • Keywords: Sturm-Louville equation, boundary value problems, spectral analysis of ordinary differential operators, transformation operator, integral representation, asymptotic formulas for eigenvalues, expansion formula, BOUNDARY-VALUE-PROBLEMS, EIGENVALUE PROBLEMS, SINGULAR POTENTIALS, SPECTRAL PROBLEMS, WAVE SPEED, OPERATORS, INTERVAL, SCATTERING, IMPEDANCE

Abstract

In this study we derive the Gelfand-Levitan-Marchenko type main integral equation of the inverse problem for the boundary value problem L and prove the uniquely solvability of the main integral equation. Further, we give the solution of the inverse problem by the spectral data and by two spectrum.