IJPAM: Volume 84, No. 1 (2013)

A CLASS OF STURM-LIOUVILLE OPERATORS WITH
EIGENPARAMETER DEPENDENT BOUNDARY
AND TRANSMISSION CONDITIONS

Erdoğan Şen1, Serkan Araci2, Mehmet Acikgoz3, Kamil Oruçoğlu4
1Department of Mathematics
Faculty of Science and Letters
Namik Kemal University
59030, Tekirdağ, TURKEY
2,3Department of Mathematics
Faculty of Science and Arts
University of Gaziantep
27310, Gaziantep, TURKEY
4Department of Mathematics Engineering
Istanbul Technical University
Maslak, 34469 Istanbul, TURKEY


Abstract. In this study, we investigate a Sturm-Liouville type problem with eigenparameter dependent boundary conditions and eigenparameter dependent transmission conditions. By establishing a new self-adjoint operator A associated with the problem, we construct fundamental solutions and obtain asymptotic formulae for its eigenvalues and fundamental solutions.

Received: December 24, 2012

AMS Subject Classification: 34L20, 35R10

Key Words and Phrases: asymptotics of eigenvalues and eigenfunctions, transmission conditions, differential operator

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DOI: 10.12732/ijpam.v84i1.11 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 1