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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 787920, 18 pages
http://dx.doi.org/10.1155/2012/787920
Research Article

On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation

1Division of Network, Vodafone Spain S. A., P. E. Castellana Norte, 28050 Madrid, Spain
2Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Received 11 September 2012; Revised 12 November 2012; Accepted 28 November 2012

Academic Editor: Ferhan Atici

Copyright © 2012 Pedro Almenar and Lucas Jódar. 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. P. Almenar and L. Jódar, “An upper bound for the distance between a zero and a critical point of a solution of a second order linear differential equation,” Computers & Mathematics with Applications, vol. 63, no. 1, pp. 310–317, 2012. View at Publisher · View at Google Scholar
  2. O. Došlý and P. Řehák, Half-Linear Differential Equations, vol. 202 of Mathematics Studies, North-Holland, Amsterdam, The Netherland, 2005.
  3. Á. Elbert, T. Kusano, and T. Tanigawa, “An oscillatory half-linear differential equation,” Archivum Mathematicum, vol. 33, no. 4, pp. 355–361, 1997.
  4. Á. Elbert, “A half-linear second order differential equation,” Colloquia Mathematica Societatis János Bolyai, vol. 30, pp. 158–180, 1979.
  5. H. J. Li and C. C. Yeh, “Sturmian comparison theorem for half-linear second-order differential equations,” Proceedings of the Royal Society of Edinburgh A, vol. 125, no. 6, pp. 1193–1204, 1995. View at Publisher · View at Google Scholar
  6. X. Yang, “On inequalities of Lyapunov type,” Applied Mathematics and Computation, vol. 134, no. 2-3, pp. 293–300, 2003. View at Publisher · View at Google Scholar
  7. C.-F. Lee, C.-C. Yeh, C.-H. Hong, and R. P. Agarwal, “Lyapunov and Wirtinger inequalities,” Applied Mathematics Letters of Rapid Publication, vol. 17, no. 7, pp. 847–853, 2004. View at Publisher · View at Google Scholar
  8. J. P. Pinasco, “Lower bounds for eigenvalues of the one-dimensional p-Laplacian,” Abstract and Applied Analysis, no. 2, pp. 147–153, 2004. View at Publisher · View at Google Scholar
  9. J. P. Pinasco, “Comparison of eigenvalues for the p-Laplacian with integral inequalities,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1399–1404, 2006. View at Publisher · View at Google Scholar
  10. P. Almenar and L. Jódar, “Improving explicit bounds for the solutions of second order linear differential equations,” Computers & Mathematics with Applications, vol. 57, no. 10, pp. 1708–1721, 2009. View at Publisher · View at Google Scholar
  11. R. A. Moore, “The behavior of solutions of a linear differential equation of second order,” Pacific Journal of Mathematics, vol. 5, pp. 125–145, 1955.