About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 738472, 19 pages
http://dx.doi.org/10.1155/2012/738472
Research Article

Perturbations of Half-Linear Euler Differential Equation and Transformations of Modified Riccati Equation

Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

Received 10 July 2012; Accepted 17 September 2012

Academic Editor: Allan Peterson

Copyright © 2012 Ondřej Došlý and Hana Funková. 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. O. Došlý and P. Řehák, Half-Linear Differential Equations, vol. 202 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2005.
  2. P. Hartman, Ordinary Differential Equations, John Wiley & Sons, New York, NY, USA, 1964.
  3. O. Došlý and H. Haladová, “Half-linear Euler differential equations in the critical case,” Tatra Mountains Mathematical Publications, vol. 48, pp. 41–49, 2011.
  4. Á. Elbert and A. Schneider, “Perturbations of the half-linear euler differential equation,” Results in Mathematics, vol. 37, no. 1-2, pp. 56–83, 2000. View at Zentralblatt MATH
  5. H. Krüger and G. Teschl, “Effective Prüfer angles and relative oscillation criteria,” Journal of Differential Equations, vol. 245, no. 12, pp. 3823–3848, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. O. Došlý and S. Fišnarová, “Two-parametric conditionally oscillatory half-linear differential equations,” Abstract and Applied Analysis, vol. 2011, Article ID 182827, 16 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. O. Došlý and M. Ünal, “Half-linear differential equations: linearization technique and its application,” Journal of Mathematical Analysis and Applications, vol. 335, no. 1, pp. 450–460, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J. Jaroš, K. Takaŝi, and T. Tanigawa, “Nonoscillation theory for second order half-linear differential equations in the framework of regular variation,” Results in Mathematics, vol. 43, no. 1-2, pp. 129–149, 2003. View at Zentralblatt MATH
  9. J. Jaroš, K. Takaŝi, and T. Tanigawa, “Nonoscillatory half-linear differential equations and generalized Karamata functions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 4, pp. 762–787, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. J. Sugie and N. Yamaoka, “Comparison theorems for oscillation of second-order half-linear differential equations,” Acta Mathematica Hungarica, vol. 111, no. 1-2, pp. 165–179, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. O. Došlý and S. Fišnarová, “Half-linear oscillation criteria: perturbation in term involving derivative,” Nonlinear Analysis, vol. 73, no. 12, pp. 3756–3766, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. O. Došlý, “Perturbations of the half-linear Euler-Weber type differential equation,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 426–440, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. T. Kusano, Y. Naito, and A. Ogata, “Strong oscillation and nonoscillation of quasilinear differential equations of second order,” Differential Equations and Dynamical Systems, vol. 2, no. 1, pp. 1–10, 1994. View at Zentralblatt MATH