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

Amirov R., Durak S.

TURKISH JOURNAL OF MATHEMATICS, cilt.45, sa.4, ss.1847-1870, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2104-40
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1847-1870
  • Anahtar Kelimeler: Inverse spectral problems, Sturm-Liouville operator, spectrum, uniqueness, STURM-LIOUVILLE OPERATORS, SPECTRAL PROBLEMS, RECONSTRUCTION, DISCONTINUITIES
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

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.