Eigenvalues and normalized eigenfunctionsof discontinuous Sturm-Liouville problem with transmission conditions
Reports on Mathematical Physics, vol.54, no.1, pp.41-56, 2004 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 54 Issue: 1
- Publication Date: 2004
- Doi Number: 10.1016/s0034-4877(04)80004-1
- Journal Name: Reports on Mathematical Physics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.41-56
- Keywords: Discontinuous boundary-value-problems, Eigenfunctions, Eigenvalues, Sturm-Liouville problems, Transmission conditions
- Ondokuz Mayıs University Affiliated: Yes
Abstract
In this study, discontinuous Sturm-Liouville problems which contain eigenvalue parameters both in equation and in the boundary conditions are investigated. We introduce an operator-theoretic interpretation, extend some classic results for regular Sturm-Liouville problems and obtain asymptotic approximate formulae for eigenvalues and normalized eigenfunctions. By modifying some techniques of [2, 6, 7] we obtain asymptotic formulae for eigenvalues and normalized eigenfunctions. In the special case, when our problem is continuous, the obtained results coincide with the corresponding results in [2].