On the Estimations of the Small Periodic Eigenvalues

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...

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Bibliographic Details
Main Authors: Seza Dinibütün, O. A. Veliev
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/145967
Description
Summary: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.
ISSN:1085-3375
1687-0409