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Journal of Mathematical Sciences

, Volume 198, Issue 3, pp 296–302 | Cite as

Oscillation of Second-Order Nonlinear Impulsive Difference Equations with Continuous Variables

  • F. Karakoç
Article
  • 64 Downloads

The paper deals with a second-order nonlinear impulsive difference equation with continuous variable. Sufficient conditions for the oscillation of impulsive difference equation are obtained by using a nonimpulsive inequality.

Keywords

Continuous Variable Difference Equation Delay Differential Equation Impulsive Differential Equation Oscillation Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. G. Zhang, J. Yan, and S. K. Choi, “Oscillation for difference equations with continuous variable,” Comput. Math. Appl., 36, No. 9, 11–18 (1998).CrossRefMathSciNetGoogle Scholar
  2. 2.
    B. G. Zhang, “Oscillation of a class of difference equations with continuous arguments,” Appl. Math. Lett., 14, 557–561 (2001).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Z. Zhang, P. Bi, and J. Chen, “Oscillation of a second order nonlinear difference equation with continuous variable,” J. Math. Anal. Appl., 255, No. 1, 349–357 (2001).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    S. Wu and Z. Hou, “Oscillation criteria for a class of neutral difference equations with continuous variable,” J. Math. Anal. Appl., 290, No. 1, 316–323 (2004).CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    B. G. Zhang and F.Y. Lian, “Oscillation criteria for certain difference equations with continuous variables,” Indian J. Pure Appl. Math., 37, No. 6, 325–341 (2006).MATHMathSciNetGoogle Scholar
  6. 6.
    P. Wang and M. Wu, “Oscillation of certain second order nonlinear damped difference equations with continuous variable,” Appl. Math. Lett., 20, No. 6, 637–644 (2007).CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    A. M. Samoilenko and N. A. Perestyuk, Impulsive differential equations, World Scientific, Singapore (1995).MATHGoogle Scholar
  8. 8.
    D. D. Bainov and P. S. Simeonov, Oscillation theory of impulsive differential equations, Int. Publ., Orlando (1998).MATHGoogle Scholar
  9. 9.
    V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of impulsive differential equations, World Scientific, Singapore (1998).Google Scholar
  10. 10.
    R. P. Agarwal, S. R. Grace, and D. O’Regan, Oscillation theory for second order dynamic equations, Taylor&Francis, New York (2003).CrossRefMATHGoogle Scholar
  11. 11.
    R. P. Agarwal, F. Karakoç, and A. Zafer, “A survey on oscillation of impulsive ordinary differential equations,” Adv. Difference Equ., Article ID 354841 (2010).Google Scholar
  12. 12.
    R. P. Agarwal and F. Karakoç, “A survey on oscillation of impulsive delay differential equations,” Comput. Math. Appl., 60, 1648–1685 (2010).CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    G. Wei and J. Shen, “Oscillation of solutions of impulsive neutral difference equations with continuous variable,” Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13, No. 1, 147–152 (2006).MATHMathSciNetGoogle Scholar
  14. 14.
    Z. Jiang, Y. Xu, and L. Lin, “Oscillation of solution of impulsive difference equation with continuous variable,” Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13, Part 2, suppl, 587–592 (2006).MathSciNetGoogle Scholar
  15. 15.
    R. P. Agarwal, F. Karakoç, and A. Zafer, “Oscillation of nonlinear impulsive partial difference equations with continuous variables,” J. Difference Equ. Appl., 18, No. 6, 1101–1114 (2012).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Ankara UniversityAnkaraTurkey

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