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Acta Mathematica Sinica

, Volume 22, Issue 5, pp 1519–1528 | Cite as

Discontinuous Sturm–Liouville Problems Containing Eigenparameter in the Boundary Conditions

  • M. Kadakal
  • O. Sh. Mukhtarov
ORIGINAL ARTICLES

Abstract

In this paper, discontinuous Sturm–Liouville problems, which contain eigenvalue parameters both in the equation and in one of the boundary conditions, are investigated. By using an operatortheoretic 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.

Keywords

Sturm–Liouville problem discontinuous boundary–value problem eigenvalue and eigenfunction eigenelement normalized eigenfunctions 

MR (2000) Subject Classification

34L20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Ondokuz Mayıs University, Science and Arts FacultyDepartment of MathematicsKurupelit 55139, SamsunTurkey
  2. 2.Gaziosmanpaşa University, Science and Arts FacultyDepartment of MathematicsTokat 60000Turkey

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