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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 182827, 16 pages
doi:10.1155/2011/182827
Research Article

Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations

Ondřej Došlý1 and Simona Fišnarová2

1Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
2Department of Mathematics, Mendel University in Brno, Zemĕdĕlská 1, 613 00 Brno, Czech Republic

Received 2 November 2010; Accepted 5 January 2011

Academic Editor: Miroslava Růžičková

Copyright © 2011 Ondřej Došlý and Simona Fišnarová. 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. E. Hille, “Non-oscillation theorems,” Transactions of the American Mathematical Society, vol. 64, pp. 234–252, 1948. View at Zentralblatt MATH
  2. T. Kusano, Y. Naito, and T. Tanigawa, “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
  3. O. Došlý and H. Haladová, “Half-linear Euler differential equations in the critical case,” to appear in Tatra Mountains Mathematical Publications.
  4. O. Došlý and S. Fišnarová, “Half-linear oscillation criteria: Perturbation in term involving derivative,” Nonlinear Analysis, Theory, Methods and Applications, vol. 73, no. 12, pp. 3756–3766, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. P. Hartman, Ordinary Differential Equations, Birkhäuser, Boston, Mass, USA, 2nd edition, 1982.
  6. F. Gesztesy and M. Ünal, “Perturbative oscillation criteria and Hardy-type inequalities,” Mathematische Nachrichten, vol. 189, pp. 121–144, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. O. Došlý and M. Ünal, “Conditionally oscillatory half-linear differential equations,” Acta Mathematica Hungarica, vol. 120, no. 1-2, pp. 147–163, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. O. Došlý and P. Řehák, Half-Linear Differential Equations, vol. 202 of North-Holland Mathematics Studies, Elsevier, Amsterdam, The Netherlands, 2005.
  9. O. Došlý and S. Fišnarová, “Variational technique and principal solution in half-linear oscillation criteria,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5385–5391, 2011. View at Publisher · View at Google Scholar