Abstract and Applied Analysis
Volume 2007 (2007), Article ID 74595, 8 pages
doi:10.1155/2007/74595
Research Article
Spectrum of a Differential Operator with Periodic Generalized Potential
Department of Mathematics, Faculty of Arts and Sciences, Gaziantep University, Gaziantep 27310, Turkey
Received 2 April 2007; Revised 11 July 2007; Accepted 5 October 2007
Academic Editor: Agacik Zafer
Copyright © 2007 Mehmet Sahin and Manaf Dzh. Manafov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study some spectral problems for a second-order differential operator with periodic potential. Notice that the given potential is a sum of zero- and first-order generalized functions. It is shown that the spectrum of the investigated operator consists of infinite number of gaps whose length limit unlike the classic case tends to nonzero constant in some place and to infinity in other place.