On the rate of the convergence of the characteristic values of an integral operator associated with a dissipative fourth order differential operator in lim-4 case with finite transmission conditions

Ugurlu E., BAYRAM E.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.52, sa.10, ss.2627-2644, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 52 Sayı: 10
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s10910-014-0404-3
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2627-2644
  • Anahtar Kelimeler: Dissipative operator, Fourth order operator, Transmission conditions, Completeness theorem, BOUNDARY-VALUE-PROBLEMS, EQUATIONS
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, our main aim is to investigate the spectral properties of a singular dissipative fourth order boundary value problem in lim-4 case with finite transmission conditions. For this purpose we construct a suitable differential operator in an appropriate Hilbert space. After showing that this differential operator is a dissipative operator we pass to the resolvent operator with an explicit form. Using this resolvent operator and Krein's theorem we prove a completeness theorem on the boundary value transmission problem.