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, vol.52, no.10, pp.2627-2644, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 10
  • Publication Date: 2014
  • Doi Number: 10.1007/s10910-014-0404-3
  • Journal Name: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2627-2644
  • Keywords: Dissipative operator, Fourth order operator, Transmission conditions, Completeness theorem, BOUNDARY-VALUE-PROBLEMS, EQUATIONS
  • Ankara University Affiliated: Yes

Abstract

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.