About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 145967, 11 pages
http://dx.doi.org/10.1155/2013/145967
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.

Linked References

  1. M. S. P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Acedemic Press, Edinburg, UK, 1973.
  2. J. Pöschel and E. Trubowitz, Inverse Spectral Theory, Academic Press, Boston, Mass, USA, 1987. View at MathSciNet
  3. A. L. Andrew, “Correction of finite element eigenvalues for problems with natural or periodic boundary conditions,” BIT, vol. 28, no. 2, pp. 254–269, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. L. Andrew, “Correction of finite difference eigenvalues of periodic Sturm-Liouville problems,” Journal of Australian Mathematical Society B, vol. 30, no. 4, pp. 460–469, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. J. Condon, “Corrected finite difference eigenvalues of periodic Sturm-Liouville problems,” Applied Numerical Mathematics, vol. 30, no. 4, pp. 393–401, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Vanden Berghe, M. Van Daele, and H. De Meyer, “A modified difference scheme for periodic and semiperiodic Sturm-Liouville problems,” Applied Numerical Mathematics, vol. 18, no. 1–3, pp. 69–78, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. X. Ji and Y. S. Wong, “Prüfer method for periodic and semi-periodic sturm-liouville eigenvalue problems,” International Journal of Computer Mathematics, vol. 39, pp. 109–123, 1991. View at Publisher · View at Google Scholar
  8. Y. S. Wong and X. Z. Ji, “On shooting algorithm for Sturm-Liouville eigenvalue problems with periodic and semi-periodic boundary conditions,” Applied Mathematics and Computation, vol. 51, no. 2-3, pp. 87–104, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. X. Z. Ji, “On a shooting algorithm for Sturm-Liouville eigenvalue problems with periodic and semi-periodic boundary conditions,” Journal of Computational Physics, vol. 111, no. 1, pp. 74–80, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. V. Malathi, M. B. Suleiman, and B. B. Taib, “Computing eigenvalues of periodic Sturm-Liouville problems using shooting technique and direct integration method,” International Journal of Computer Mathematics, vol. 68, no. 1-2, pp. 119–132, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. O. A. Veliev and M. T. Duman, “The spectral expansion for a nonself-adjoint Hill operator with a locally integrable potential,” Journal of Mathematical Analysis and Applications, vol. 265, no. 1, pp. 76–90, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Avron and B. Simon, “The asymptotics of the gap in the Mathieu equation,” Annals of Physics, vol. 134, no. 1, pp. 76–84, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet