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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 458275, 11 pages
http://dx.doi.org/10.1155/2011/458275
Research Article

Oscillation of Second-Order Sublinear Impulsive Differential Equations

Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

Received 25 January 2011; Accepted 27 February 2011

Academic Editor: Josef Diblík

Copyright © 2011 A. Zafer. 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. T. Kusano and H. Onose, “Nonlinear oscillation of a sublinear delay equation of arbitrary order,” Proceedings of the American Mathematical Society, vol. 40, pp. 219–224, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. H. E. Gollwitzer, “On nonlinear oscillations for a second order delay equation,” Journal of Mathematical Analysis and Applications, vol. 26, pp. 385–389, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. V. N. Sevelo and O. N. Odaric, “Certain questions on the theory of the oscillation (non-oscillation) of the solutions of second order differential equations with retarded argument,” Ukrainskii Matematicheskii Zhurnal, vol. 23, pp. 508–516, 1971 (Russian).
  4. S. Belohorec, “Two remarks on the properties of solutions of a nonlinear differential equation,” Acta Facultatis Rerum Naturalium Universitatis Comenianae/Mathematica, vol. 22, pp. 19–26, 1969.
  5. D. D. Bainov, Yu. I. Domshlak, and P. S. Simeonov, “Sturmian comparison theory for impulsive differential inequalities and equations,” Archiv der Mathematik, vol. 67, no. 1, pp. 35–49, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. Gopalsamy and B. G. Zhang, “On delay differential equations with impulses,” Journal of Mathematical Analysis and Applications, vol. 139, no. 1, pp. 110–122, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Yan, “Oscillation properties of a second-order impulsive delay differential equation,” Computers & Mathematics with Applications, vol. 47, no. 2-3, pp. 253–258, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Yong-shao and F. Wei-zhen, “Oscillations of second order nonlinear ODE with impulses,” Journal of Mathematical Analysis and Applications, vol. 210, no. 1, pp. 150–169, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  9. Z. He and W. Ge, “Oscillations of second-order nonlinear impulsive ordinary differential equations,” Journal of Computational and Applied Mathematics, vol. 158, no. 2, pp. 397–406, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. C. Huang, “Oscillation and nonoscillation for second order linear impulsive differential equations,” Journal of Mathematical Analysis and Applications, vol. 214, no. 2, pp. 378–394, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Luo, “Second-order quasilinear oscillation with impulses,” Computers & Mathematics with Applications, vol. 46, no. 2-3, pp. 279–291, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. Özbekler and A. Zafer, “Sturmian comparison theory for linear and half-linear impulsive differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 63, no. 5–7, pp. e289–e297, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. A. Özbekler and A. Zafer, “Picone's formula for linear non-selfadjoint impulsive differential equations,” Journal of Mathematical Analysis and Applications, vol. 319, no. 2, pp. 410–423, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. G. Ballinger and X. Liu, “Permanence of population growth models with impulsive effects,” Mathematical and Computer Modelling, vol. 26, no. 12, pp. 59–72, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Z. Lu, X. Chi, and L. Chen, “Impulsive control strategies in biological control of pesticide,” Theoretical Population Biology, vol. 64, no. 1, pp. 39–47, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. J. Sun, F. Qiao, and Q. Wu, “Impulsive control of a financial model,” Physics Letters A, vol. 335, no. 4, pp. 282–288, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. S. Tang and L. Chen, “Global attractivity in a “food-limited” population model with impulsive effects,” Journal of Mathematical Analysis and Applications, vol. 292, no. 1, pp. 211–221, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. Tang, Y. Xiao, and D. Clancy, “New modelling approach concerning integrated disease control and cost-effectivity,” Nonlinear Analysis: Theory, Methods & Applications, vol. 63, no. 3, pp. 439–471, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Teaneck, NJ, USA, 1989.
  20. A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific, River Edge, NJ, USA, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. Akhmetov and R. Sejilova, “The control of the boundary value problem for linear impulsive integro-differential systems,” Journal of Mathematical Analysis and Applications, vol. 236, no. 2, pp. 312–326, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. D. Bainov and V. Covachev, Impulsive Differential Equations with a Small Parameter, vol. 24 of Series on Advances in Mathematics for Applied Sciences, World Scientific, River Edge, NJ, USA, 1994.