Discontinuous Sturm-Liouville problems containing eigenparameter in the boundary conditions

Kadakal M., Mukhtarov O. S.

ACTA MATHEMATICA SINICA-ENGLISH SERIES, vol.22, no.5, pp.1519-1528, 2006 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 5
  • Publication Date: 2006
  • Doi Number: 10.1007/s10114-005-0751-x
  • Journal Name: ACTA MATHEMATICA SINICA-ENGLISH SERIES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1519-1528
  • Keywords: Sturm-Liouville problem, discontinuous boundary-value problem, eigenvalue and eigenfunction, eigenelement, normalized eigenfunctions, EIGENVALUE PARAMETER
  • Ondokuz Mayıs University Affiliated: No

Abstract

In this paper, discontinuous Sturm-Liouville problems, which contain eigenvalue parameters both in the equation and in one of the boundary conditions, axe investigated. By using an operator-theoretic interpretation we extend some classic results for regular Sturm-Liouville problems and obtain asymptotic approximate formulae for eigenvalues and normalized eigenfunctions. We modify some techniques of [Fulton, C. T., Proc. Roy. Soc. Edin. 77 (A), 293-308 (1977)], [Walter, J., Math. Z., 133, 301-312 (1973)] and [Titchmarsh, E. C., Eigenfunctions Expansion Associated with Second Order Differential Equations I, 2nd edn., Oxford Univ. Pres, London, 1962], then by using these techniques we obtain asymptotic formulae for eigenelement norms and normalized eigenfunctions.