Electron. J. Differential Equations, Vol. 2017 (2017), No. 95, pp. 1-13.

Dissipative Sturm-Liouville operators with a spectral parameter in the boundary condition on bounded time scales

Bilender P. Allahverdiev, Aytekin Eryilmaz, Huseyin Tuna

Abstract:
In this article we consider a second-order Sturm-Liouville operator with a spectral parameter in the boundary condition on bounded time scales. We construct a selfadjoint dilation of the dissipative Sturm-Liouville operators. Using by methods of Pavlov [40,41,42], we prove the completeness of the system of eigenvectors and associated vectors of the dissipative Sturm-Liouville operators on bounded time scales.

Submitted February 29, 2016. Published April 5, 2017.
Math Subject Classifications: 47A20, 47A40, 47A45, 34B05, 34B10, 39A10.
Key Words: Time scale; delta-differentiable; dilation; dissipative operator; system of eigenvectors; scattering matrix; functional model; characteristic function.

Show me the PDF file (274 KB), TEX file for this article.

Bilender P. Allahverdiev
Department of Mathematics
Faculty of Arts and Science
Süleyman Demirel University
32260 Isparta, Turkey
email: bilenderpasaoglu@sdu.edu.tr
Aytekin Eryilmaz
Department of Mathematics
Nevsehir University
Nevsehir, Turkey
email: eryilmazaytekin@gmail.com
Hüseyin Tuna
Department of Mathematics
Mehmet Akif Ersoy University
Burdur, Turkey
email: hustuna@gmail.com

Return to the EJDE web page