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Mediterranean Journal of Mathematics

, Volume 11, Issue 2, pp 463–475 | Cite as

Oscillation Theorems for Fourth-Order Half-Linear Delay Dynamic Equations with Damping

  • Ravi P. Agarwal
  • Martin Bohner
  • Tongxing Li
  • Chenghui Zhang
Article

Abstract

This article is concerned with oscillatory behavior of a class of fourth-order half-linear delay dynamic equations with damping on a time scale. Some new oscillation criteria are established.

Mathematics Subject Classification (2010)

34K11 34N05 39A10 

Keywords

Oscillatory solution delay equation dynamic equation with damping fourth-order equation time scale 

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References

  1. 1.
    Agarwal R.P., Bohner M., Tang S., Li T., Zhang C.: Oscillation and asymptotic behavior of third-order nonlinear retarded dynamic equations. Appl. Math. Comput. 219, 3600–3609 (2012)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Agarwal R.P., Grace S.R., O’Regan D.: Oscillation Theory for Second Order Dynamic Equations, Series in Mathematical Analysis and Applications, vol. 5. Taylor and Francis Ltd, London (2003)CrossRefGoogle Scholar
  3. 3.
    Agarwal R.P., O’Regan D., Saker S.H.: Oscillation of second order nonlinear neutral delay dynamic equations on time scales. J. Math. Anal. Appl. 300, 203–217 (2004)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Akın-Bohner E., Bohner M., Saker S.H.: Oscillation criteria for a certain class of second order Emden–Fowler dynamic equations. Electron. Trans. Numer. Anal. 27, 1–12 (2007)MATHMathSciNetGoogle Scholar
  5. 5.
    Bohner M., Peterson A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston (2001)CrossRefMATHGoogle Scholar
  6. 6.
    Bohner M., Peterson A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003)CrossRefMATHGoogle Scholar
  7. 7.
    Erbe L., Hassan T.S., Peterson A.: Oscillation criteria for nonlinear damped dynamic equations on time scales. Appl. Math. Comput. 203, 343–357 (2008)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Erbe L., Peterson A., Saker S.H.: Hille and Nehari type criteria for third-order dynamic equations. J. Math. Anal. Appl. 329, 112–131 (2007)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Grace S.R., Agarwal R.P., Pinelas S.: On the oscillation of fourth order superlinear dynamic equations on time scales. Dynam. Syst. Appl. 20, 45–54 (2011)MATHMathSciNetGoogle Scholar
  10. 10.
    Grace S.R., Agarwal R.P., Sae-jie W.: Monotone and oscillatory behavior of certain fourth order nonlinear dynamic equations. Dynam. Syst. Appl. 19, 25–32 (2010)MATHMathSciNetGoogle Scholar
  11. 11.
    Grace S.R., Bohner M., Sun S.: Oscillation of fourth-order dynamic equations. Hacet. J. Math. Stat. 39, 545–553 (2010)MATHMathSciNetGoogle Scholar
  12. 12.
    Hassan T.S.: Oscillation of third order nonlinear delay dynamic equations on time scales. Math. Comput. Modelling 49, 1573–1586 (2009)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Hilger S.: Analysis on measure chains–a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Li T., Agarwal R.P., Bohner, M.: Some oscillation results for second-order neutral dynamic equations. Hacet. J. Math. Stat. 41, 715–721 (2012)Google Scholar
  15. 15.
    Li T., Han Z., Sun S., Zhao Y.: Oscillation results for third order nonlinear delay dynamic equations on time scales. Bull. Malays. Math. Sci. Soc. 34, 639–648 (2011)MATHMathSciNetGoogle Scholar
  16. 16.
    Li T., Thandapani E., Tang S.: Oscillation theorems for fourth-order delay dynamic equations on time scales. Bull. Math. Anal. Appl. 3, 190–199 (2011)MathSciNetGoogle Scholar
  17. 17.
    Saker S.H.: Oscillation Theory of Dynamic Equations on Time Scales, Second and Third Orders. Lambert Academic Publisher (2010)Google Scholar
  18. 18.
    Saker S.H., Agarwal R.P., O’Regan D.: Oscillation of second-order damped dynamic equations on time scales. J. Math. Anal. Appl. 330, 1317–1337 (2007)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Zhang B., Zhu S.: Oscillation of second order nonlinear delay dynamic equations on time scales. Comput. Math. Appl. 49, 599–609 (2005)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Zhang C., Li T., Agarwal R.P., Bohner M.: Oscillation results for fourth-order nonlinear dynamic equations. Appl. Math. Lett. 25, 2058–2065 (2012)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
  • Martin Bohner
    • 2
  • Tongxing Li
    • 3
  • Chenghui Zhang
    • 3
  1. 1.Department of MathematicsTexas A&M UniversityKingsvilleUSA
  2. 2.Department of Mathematics and StatisticsMissouri S&TRollaUSA
  3. 3.School of Control Science and EngineeringShandong UniversityJinanP. R. China

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