Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2009 (2009), Article ID 109757, 27 pages
http://dx.doi.org/10.1155/2009/109757
Research Article

Various Half-Eigenvalues of Scalar -Laplacian with Indefinite Integrable Weights

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received 1 May 2009; Accepted 28 June 2009

Academic Editor: Pavel Drabek

Copyright © 2009 Wei Li and Ping Yan. 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. G. Meng, P. Yan, and M. Zhang, “Spectrum of one-dimensional p-Laplacian with an indefinite intergrable weight,” to appear in Mediterranean Journal of Mathematics.
  2. A. Anane, O. Chakrone, and M. Monssa, “Spectrum of one dimensional p-Laplacian with in-definite weight,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2002, no. 17, pp. 1–11, 2002. View at Google Scholar
  3. M. Cuesta, “Eigenvalue problems for the p-Laplacian with indefinite weights,” Electronic Journal of Differential Equations, vol. 2001, no. 33, pp. 1–9, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. W. Eberhard and Á. Elbert, “On the eigenvalues of half-linear boundary value problems,” Mathematische Nachrichten, vol. 213, pp. 57–76, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. A. Binding and B. P. Rynne, “Oscillation and interlacing for various spectra of p-Laplacian,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2780–2791, 2009. View at Publisher · View at Google Scholar
  6. P. A. Binding and B. P. Rynne, “Variational and non-variational eigenvalues of the p-Laplacian,” Journal of Differential Equations, vol. 244, no. 1, pp. 24–39, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. Zettl, Sturm-Liouville Theory, vol. 121 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2005. View at MathSciNet
  8. M. Zhang, “Continuity in weak topology: higher order linear systems of ODE,” Science in China, vol. 51, no. 6, pp. 1036–1058, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Zhang, “Extremal values of smallest eigenvalues of Hill's operators with potentials in L1 balls,” Journal of Differential Equations, vol. 246, no. 11, pp. 4188–4220, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. P. Yan and M. Zhang, “Continuity in weak topology and extremal problems of eigenvalues of the p-Laplacian,” to appear in Transactions of the American Mathematical Society.
  11. W. Li and P. Yan, “Continuity and continuous differentiability of half-eigenvalues in potentials,” preprint.
  12. V. I. Arnol'd, Mathematical Methods of Classical Mechanics, vol. 60 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2nd edition, 1989. View at MathSciNet
  13. H. Broer and M. Levi, “Geometrical aspects of stability theory for Hill's equations,” Archive for Rational Mechanics and Analysis, vol. 131, no. 3, pp. 225–240, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Zhang, “The rotation number approach to eigenvalues of the one-dimensional p-Laplacian with periodic potentials,” Journal of the London Mathematical Society, vol. 64, no. 1, pp. 125–143, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. R. E. Megginson, An Introduction to Banach Space Theory, vol. 183 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1998. View at MathSciNet
  16. J. K. Hale, Ordinary Differential Equations, vol. 20 of Pure and Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1969. View at MathSciNet