ASYMPTOTIC PROPERTIES OF EIGENVALUES AND EIGENFUNCTIONS OF A STURM-LIOUVILLE PROBLEM WITH DISCONTINUOUS WEIGHT FUNCTION


ŞEN E.

MISKOLC MATHEMATICAL NOTES, vol.15, no.1, pp.197-209, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.18514/mmn.2014.706
  • Title of Journal : MISKOLC MATHEMATICAL NOTES
  • Page Numbers: pp.197-209

Abstract

In this paper, we extend some spectral properties of regular Sturm-Liouville problems to those which consist of a Sturm-Liouville equation with discontinuous weight at two interior points together with spectral parameter-dependent boundary conditions. By modifying some techniques of [C. T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977) 293-308; O. Sh. Mukhtarov and M. Kadakal, Some spectral properties of one Sturm-Liouville type problem with discontinuous weight, Siberian Mathematical Journal, 46 (2005) 681-694], we give an operator-theoretic formulation for the considered problem and obtain asymptotic formulas for the eigenvalues and eigenfunctions.