Half inverse problems for the impulsive quadratic pencil with the discontinouty coefficient


AMİROV R. , DURAK S.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.4, pp.1847-1870, 2021 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2104-40
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1847-1870
  • Keywords: Inverse spectral problems, Sturm-Liouville operator, spectrum, uniqueness, STURM-LIOUVILLE OPERATORS, SPECTRAL PROBLEMS, RECONSTRUCTION, DISCONTINUITIES

Abstract

In this paper, we study the inverse spectral problem for the quadratic differential pencils with discontinuity coefficient on [0, pi] with separable boundary conditions and the impulsive conditions at the point x = pi/2 . We prove that two potential functions on the interval [0, pi], and the parameters in the boundary and impulsive conditions can be determined from a sequence of eigenvalues for two cases: (i) The potentials are given on (0, pi/4 (1 + alpha) , (ii) The potentials are given on (pi/4 (1 + alpha) , pi) , where 0 < alpha < 1, respectively.