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

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.

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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

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