Asymptotic formulas for eigenfunctions of the Sturm-Liouville problems with eigenvalue parameter in the boundary conditions

Altınışık N., Mukhtarov O. S., Kadakal M.

KUWAIT JOURNAL OF SCIENCE & ENGINEERING, cilt.39, sa.1A, ss.1-17, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 1A
  • Basım Tarihi: 2012
  • Dergi Adı: KUWAIT JOURNAL OF SCIENCE & ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1-17
  • Anahtar Kelimeler: Discontinuous Sturm-Liouville problem, transmission conditions, the asymptotic of eigenvalues, discontinuous boundary value problem
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this study, discontinuous Sturm-Liouville problems with eigenvalue parameter in the boundary conditions and with transmission conditions at the point of discontinuity are considered. We construct some basic solutions, derive an asymptotic expression for these solutions and suggest a new approach for the definition of a suitable Hilbert space and a symmetric linear operator defined in this space in such a way that the considered problem can be interpreted as the eigenvalue problem of this operator. By using these results we find asymptotic formulas for eigenvalues and corresponding eigenfunctions.