Advertisement

Oscillation of Emden–Fowler type nonlinear neutral delay dynamic equation on time scales

  • Ying Sui
  • Shurong SunEmail author
Original Research
  • 67 Downloads

Abstract

In this paper, we consider the following Emden–Fowler type nonlinear neutral delay dynamic equation of the form
$$\begin{aligned} \left( r(t)\left( (y(t)+p(t)y(\tau (t)))^\Delta \right) ^\alpha \right) ^\Delta +q(t)y^\beta (m(t))=0 \end{aligned}$$
on time scales, where \(\alpha \) and \(\beta \) are ratios of two odd positive integers. Specially, \(\alpha \), \(\beta \) are arbitrary and without any conditional restrictions, which are completely new compared with previous references. Some new oscillatory and asymptotic properties are obtained by means of inequality technique and Riccati transformation. The results obtained generalize and improve some of the results of Agarwal and Džurina et al.

Keywords

Oscillation Neutral Time scales Dynamic equation 

Mathematics Subject Classification

34C10 34K40 26E70 

References

  1. 1.
    Hilger, S.: Analysis on measure chains a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: Oscillation criteria for second-order dynamic equations on time scales. Appl. Math. Lett. 31, 34–40 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Grace, S.R., Graef, J., El-Beltagy, M.: On the oscillation of third order neutral delay dynamic equations on time scales. Comput. Math. Appl. 63, 775–782 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Hassan, T.S.: Oscillation of third order nonlinear delay dynamic equations on time scales. Math. Comput. Model. 49, 1573–1586 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Han, Z.L., Sun, S., Shi, B.: Oscillation criteria for a class of second-order Emden–Fowler delay dynamic equations on time scales. J. Math. Anal. Appl. 334, 847–858 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Sun, S.R., Han, Z., Zhao, P., Zhang, C.: Oscillation for a class of second-order Emden–Fowler delay dynamic equations on time scales. Adv. Differ. Equ. 334, 847–858 (2009)MathSciNetGoogle Scholar
  7. 7.
    Chen, D.X.: Oscillation of second-order Emden–Fowler neutral delay dynamic equations on time scales. Math. Comput. Model. 51, 1221–1229 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Agarwala, R.P., Zhang, C., Li, T.: Some remarks on oscillation of second order neutral differential equations. Appl. Math. Comput. 274, 178–181 (2016)MathSciNetGoogle Scholar
  9. 9.
    Džurina, J., Jadlovská, I.: A note on oscillation of second-order delay differential equations. Appl. Math. Lett. 69, 126–132 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Thandapani, E., Piramanantham, V., Pinelas, S.: Oscillation criteria for second-order neutral delay dynamic equations with mixed nonlinearities. Adv. Differ. Equ. 2011, 1–14 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Chen, D.: Oscillation of second-order Emden–Fowler neutral delay dynamic equations on time scales. Math. Comput. Model. 51, 1221–1229 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Erbe, L., Hassan, T., Peterson, A.: Oscillation criteria for nonlinear damped dynamic equations on time scales. Appl. Math. Comput. 203, 343–357 (2008)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003)CrossRefzbMATHGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of JinanJinanChina

Personalised recommendations