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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 47 Issue: 2

Kamenev-type criteria for nonlinear second-order delay dynamic equations

M. Tamer Şenel
Nadide Utku
M. M. A. El-sheikh
Tongxing Li
Pages
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Publication Date
2018-04-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These criteria improve some related results for second-order differential equations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We study oscillation of certain second-order nonlinear delay dynamic equations on arbitrary time scales.
📊
Key Findings & Data:Employing a class of kernel functions, new Kamenev-type oscillation criteria are presented that differ from the known ones.
💡
Conclusion & Impact:These criteria improve some related results for second-order differential equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Oscillation · Second-order dynamic equation · Delay dynamic equation

Abstract

We study oscillation of certain second-order nonlinear delay dynamic equations on arbitrary time scales. Employing a class of kernel functions, new Kamenev-type oscillation criteria are presented that differ from the known ones. These criteria improve some related results for second-order differential equations.

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Cite This Article

Şenel, M. T., Utku, N., El-sheikh, M. M. A., Li, T. (2018). Kamenev-type criteria for nonlinear second-order delay dynamic equations. Hacettepe Journal of Mathematics and Statistics, Volume: 47 Issue: 2. https://ajindex.com/articles/1402953

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References (33)

  1. Agarwal, R. P., Bohner, M., and Li, T. Oscillatory behavior of second-order half-linear damped dynamic equations, Appl. Math. Comput. 254, 408–418, 2015.
  2. Agarwal, R. P., Bohner, M., Li, T., and Zhang, C. Oscillation criteria for second-order dynamic equations on time scales, Appl. Math. Lett. 31, 34–40, 2014.
  3. Agarwal, R. P., Bohner, M., O’Regan, D., and Peterson, A. Dynamic equations on time scales: a survey, J. Comput. Appl. Math. 141, 1–26, 2002.
  4. Agarwal, R. P., Bohner, M., and Saker, S. H. Oscillation of second order delay dynamic equations, Can. Appl. Math. Q. 13, 1–17, 2005.
  5. Agarwal, R. P., Grace, S. R., and O’Regan, D. Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations (Kluwer Academic Publishers, Dordrecht, 2002).
  6. Bohner, M., Hassan, T. S., and Li, T. Fite–Hille–Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments, Indag. Math. (N.S.) 29, 548–560, 2018.
  7. Bohner, M. and Li, T. Oscillation of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient, Appl. Math. Lett. 37, 72–76, 2014.
  8. Bohner, M. and Li, T. Kamenev-type criteria for nonlinear damped dynamic equations, Sci. China Math. 58, 1445–1452, 2015.
  9. Bohner, M. and Peterson, A. Dynamic Equations on Time Scales: An Introduction with Applications (Birkhäuser, Boston, 2001).
  10. Bohner, M. and Peterson, A. Advances in Dynamic Equations on Time Scales (Birkhäuser, Boston, 2003).
  11. Braverman, E. and Karpuz, B. Nonoscillation of second-order dynamic equations with several delays, Abstr. Appl. Anal. 2011, 1–34, 2011.
  12. Candan, T. Oscillation criteria for second-order nonlinear neutral dynamic equations with distributed deviating arguments on time scales, Adv. Difference Equ. 2013, 1–8, 2013.
  13. Erbe, L., Peterson, A., and Saker, S. H. Oscillation criteria for second-order nonlinear delay dynamic equations, J. Math. Anal. Appl. 333, 505–522, 2007.
  14. Fu, Y.-L. and Wang, Q.-R. Oscillation criteria for second-order nonlinear damped differential equations, Dynam. Systems Appl. 18, 375–391, 2009.
  15. Grace, S. R., Bohner, M., and Sun, S. Oscillation of fourth-order dynamic equations, Hacet. J. Math. Stat. 39, 545–553, 2010.
  16. Grace, S. R. and Zafer, A. Oscillation of fourth-order nonlinear neutral delay dynamic equations, Hacet. J. Math. Stat. 44, 331–339, 2015.
  17. Hilger, S. Analysis on measure chains–a unified approach to continuous and discrete calculus, Results Math. 18, 18–56, 1990.
  18. Huang, Y. and Meng, F. Oscillation criteria for forced second-order nonlinear differential equations with damping, J. Comput. Appl. Math. 224, 339–345, 2009.
  19. Karpuz, B. Li type oscillation theorem for delay dynamic equations, Math. Methods Appl. Sci. 36, 993–1002, 2013.
  20. Karpuz, B. and Öcalan, Ö. New oscillation tests and some refinements for first-order delay dynamic equations, Turkish J. Math. 40, 850–863, 2016.
  21. Li, T., Agarwal, R. P., and Bohner, M. Some oscillation results for second-order neutral dynamic equations, Hacet. J. Math. Stat. 41, 715–721, 2012.
  22. Li, T. and Saker, S. H. A note on oscillation criteria for second-order neutral dynamic equations on isolated time scales, Commun. Nonlinear Sci. Numer. Simul. 19, 4185–4188, 2014.
  23. Li, T. and Rogovchenko, Yu. V. Oscillation criteria for second-order superlinear Emden– Fowler neutral differential equations, Monatsh. Math. 184, 489–500, 2017.
  24. Liu, L. and Bai, Y. New oscillation criteria for second-order nonlinear neutral delay differential equations, J. Comput. Appl. Math. 231, 657–663, 2009.
  25. Long, Q. and Wang, Q.-R. New oscillation criteria of second-order nonlinear differential equations, Appl. Math. Comput. 212, 357–365, 2009.
  26. Meng, F. and Huang, Y. Interval oscillation criteria for a forced second-order nonlinear differential equation with damping, Appl. Math. Comput. 218, 1857–1861, 2011.
  27. O’Regan, D. and Hassan, T. S. Oscillation criteria for solutions to nonlinear dynamic equations of higher order, Hacet. J. Math. Stat. 45, 417–427, 2016.
  28. Sahiner, Y. Oscillation of second-order delay differential equations on time scales, Nonlinear Anal. 63, e1073–e1080, 2005.
  29. Senel, M. T. Kamenev-type oscillation criteria for the second-order nonlinear dynamic equations with damping on time scales, Abstr. Appl. Anal. 2012, 1–18, 2012.
  30. Sun, Y. G. New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping, J. Math. Anal. Appl. 291, 341–351, 2004.
  31. Utku, N., Li, T., and Senel, M. T. An asymptotic criterion for third-order dynamic equations with positive and negative coefficients, Hacet. J. Math. Stat. 44, 1157–1162, 2015.
  32. Xu, R. and Meng, F. New Kamenev-type oscillation criteria for second order neutral nonlinear differential equations, Appl. Math. Comput. 188, 1364–1370, 2007.
  33. Zafer, A. On oscillation and nonoscillation of second-order dynamic equations, Appl. Math. Lett. 22, 136–141, 2009.