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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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)
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)
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)
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)
Bohner M., Peterson A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston (2001)
Bohner M., Peterson A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003)
Erbe L., Hassan T.S., Peterson A.: Oscillation criteria for nonlinear damped dynamic equations on time scales. Appl. Math. Comput. 203, 343–357 (2008)
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)
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)
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)
Grace S.R., Bohner M., Sun S.: Oscillation of fourth-order dynamic equations. Hacet. J. Math. Stat. 39, 545–553 (2010)
Hassan T.S.: Oscillation of third order nonlinear delay dynamic equations on time scales. Math. Comput. Modelling 49, 1573–1586 (2009)
Hilger S.: Analysis on measure chains–a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)
Li T., Agarwal R.P., Bohner, M.: Some oscillation results for second-order neutral dynamic equations. Hacet. J. Math. Stat. 41, 715–721 (2012)
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)
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)
Saker S.H.: Oscillation Theory of Dynamic Equations on Time Scales, Second and Third Orders. Lambert Academic Publisher (2010)
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)
Zhang B., Zhu S.: Oscillation of second order nonlinear delay dynamic equations on time scales. Comput. Math. Appl. 49, 599–609 (2005)
Zhang C., Li T., Agarwal R.P., Bohner M.: Oscillation results for fourth-order nonlinear dynamic equations. Appl. Math. Lett. 25, 2058–2065 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Agarwal, R.P., Bohner, M., Li, T. et al. Oscillation Theorems for Fourth-Order Half-Linear Delay Dynamic Equations with Damping. Mediterr. J. Math. 11, 463–475 (2014). https://doi.org/10.1007/s00009-013-0310-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-013-0310-0