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Abstract and Applied Analysis
Volume 2013, Article ID 145967, 11 pages
Research Article

On the Estimations of the Small Periodic Eigenvalues

Department of Mathematics, Dogus University, Acıbadem, Kadiköy, 81010 Istanbul, Turkey

Received 15 April 2013; Revised 13 June 2013; Accepted 16 June 2013

Academic Editor: Ferhan M. Atici

Copyright © 2013 Seza Dinibütün and O. A. Veliev. 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.


We estimate the small periodic and semiperiodic eigenvalues of Hill's operator with sufficiently differentiable potential by two different methods. Then using it we give the high precision approximations for the length of th gap in the spectrum of Hill-Sehrodinger operator and for the length of th instability interval of Hill's equation for small values of Finally we illustrate and compare the results obtained by two different ways for some examples.