Spectral Properties of Discontinuous Sturm-Liouville Problems with a Finite Number of Transmission Conditions


ŞEN E., Mukhtarov O. S.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.13, no.1, pp.153-170, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1007/s00009-014-0487-x
  • Title of Journal : MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Page Numbers: pp.153-170

Abstract

In this paper we investigate discontinuous two-point boundary value problems with eigenparameter in the boundary conditions and with transmission conditions at the finitely many points of discontinuity. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of the considered problem coincide with those of A. We obtain asymptotic formulas for the eigenvalues and eigenfunctions. Also we show that the eigenelements of A are complete in H.