Research Article

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

Volume: 47 Number: 2 April 1, 2018
EN

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

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.

Keywords

References

  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.
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  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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

April 1, 2018

Submission Date

July 10, 2016

Acceptance Date

February 8, 2017

Published in Issue

Year 2018 Volume: 47 Number: 2

APA
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, 47(2), 339-345. https://izlik.org/JA96SA43KH
AMA
1.Şenel MT, Utku N, El-sheikh MMA, Li T. Kamenev-type criteria for nonlinear second-order delay dynamic equations. Hacettepe Journal of Mathematics and Statistics. 2018;47(2):339-345. https://izlik.org/JA96SA43KH
Chicago
Şenel, M. Tamer, Nadide Utku, M. M. A. El-sheikh, and Tongxing Li. 2018. “Kamenev-Type Criteria for Nonlinear Second-Order Delay Dynamic Equations”. Hacettepe Journal of Mathematics and Statistics 47 (2): 339-45. https://izlik.org/JA96SA43KH.
EndNote
Şenel MT, Utku N, El-sheikh MMA, Li T (April 1, 2018) Kamenev-type criteria for nonlinear second-order delay dynamic equations. Hacettepe Journal of Mathematics and Statistics 47 2 339–345.
IEEE
[1]M. T. Şenel, N. Utku, M. M. A. El-sheikh, and T. Li, “Kamenev-type criteria for nonlinear second-order delay dynamic equations”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 2, pp. 339–345, Apr. 2018, [Online]. Available: https://izlik.org/JA96SA43KH
ISNAD
Şenel, M. Tamer - Utku, Nadide - El-sheikh, M. M. A. - Li, Tongxing. “Kamenev-Type Criteria for Nonlinear Second-Order Delay Dynamic Equations”. Hacettepe Journal of Mathematics and Statistics 47/2 (April 1, 2018): 339-345. https://izlik.org/JA96SA43KH.
JAMA
1.Şenel MT, Utku N, El-sheikh MMA, Li T. Kamenev-type criteria for nonlinear second-order delay dynamic equations. Hacettepe Journal of Mathematics and Statistics. 2018;47:339–345.
MLA
Şenel, M. Tamer, et al. “Kamenev-Type Criteria for Nonlinear Second-Order Delay Dynamic Equations”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 2, Apr. 2018, pp. 339-45, https://izlik.org/JA96SA43KH.
Vancouver
1.M. Tamer Şenel, Nadide Utku, M. M. A. El-sheikh, Tongxing Li. Kamenev-type criteria for nonlinear second-order delay dynamic equations. Hacettepe Journal of Mathematics and Statistics [Internet]. 2018 Apr. 1;47(2):339-45. Available from: https://izlik.org/JA96SA43KH