BibTex RIS Cite

Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations

Year 2013, Volume: 42 Issue: 2 , 131 - 138 , 01.02.2013
https://izlik.org/JA57DW28JR

Abstract

In this paper, some new oscillation criteria are obtained for the secondorder quasi-linear neutral delay differential equationr(t)| x(t) + p(t)x(τ (t)) |α−1x(t) + p(t)x(τ (t))+ f t, x(σ(t)) = 0, t ≥ tunder the case when∞ t r α (t) ment some known results in the literature. An example is also providedto illustrate the main results.

References

  • J. K. Hale, Theory of Functional Differential Equations, Spring-Verlag, New York, 1977. R. P. Agarwal, S. L. Shieh, C. C. Yeh, Oscillation criteria for second order retarded differential equations, Math. Comput. Modelling 26, 1–11, 1997.
  • J. L. Chern, W. Ch. Lian, C. C. Yeh, Oscillation criteria for second order half-linear differential equations with functional arguments, Publ. Math. Debrecen 48, 209–216, 1996. J. Dˇ zurina, I. P. Stavroulakis, Oscillation criteria for second-order delay differential equations, Appl. Math. Comput. 140, 445–453, 2003.
  • T. Kusano, N. Yoshida, Nonoscillation theorems for a class of quasilinear differential equations of second-order, J. Math. Anal. Appl. 189, 115–127, 1995.
  • T. Kusano, Y. Naito, Oscillation and nonoscillation criteria for second order quasilinear differential equations, Acta Math. Hungar. 76, 81–99, 1997.
  • D. D. Mirzov, On the oscillation of solutions of a system of differential equations, Math. Zametki 23, 401–404, 1978.
  • J. Dˇ zurina, D. Hud´ akov´ a, Oscillation of second order neutral delay differential equations, Math. Bohem. 134, 31–38, 2009.
  • B. Bacul´ıkov´ a, D. Lackov´ a, Oscillation criteria for second order retarded differential equations, Studies of the University of Zilina, Mathematical Series. 20, 11–18, 2006.
  • B. Bacul´ıkov´ a, J. Dˇ zurina, Oscillation of third-order neutral differential equations, Math. Comput. Modelling 52, 215–226, 2010.
  • L. Liu, Y. Bai, New oscillation criteria for second-order nonlinear neutral delay differential equations, J. Comput. Math. Appl. 231, 657–663, 2009.
  • R. Xu, F. Meng, Some new oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput. 182, 797–803, 2006.
  • J. G. Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Comput. Math. Appl. 59, 3710–3717, 2010.
  • L. H. Ye, Z. T. Xu, Oscillation criteria for second-order quasilinear neutral delay differential equations, Appl. Math. Comput. 207, 388–396, 2009.
  • Z. Han, T. Li, S. Sun, Y. Sun, Remarks on the paper [Appl. Math. Comput. 207 (2009) 388–396], Appl. Math. Comput. 215, 3998–4007, 2010.
  • Z. Han, T. Li, S. Sun, W. Chen, On the oscillation of second-order neutral delay differential equations, Adv. Differ. Equ. 2010, 1–8, 2010.
  • Z. Han, T. Li, S. Sun, W. Chen, Oscillation criteria for second-order nonlinear neutral delay differential equations, Adv. Differ. Equ. 2010, 1–23, 2010.
  • T. Li, Z. Han, P. Zhao, S. Sun, Oscillation of even-order neutral delay differential equations, Adv. Differ. Equ. 2010, 1–9, 2010.
  • Z. Han, T. Li, S. Sun, W. Chen, Oscillation of second order quasilinear neutral delay differential equations, J. Appl. Math. Comput. 40, 143–152, 2012.
  • T. Li, Z. Han, C. Zhang, S. Sun, On the oscillation of second-order Emden-Fowler neutral differential equations, J. Appl. Math. Comput. 37, 601–610, 2011.
  • S. Sun, T. Li, Z. Han, Y. Sun, Oscillation of second-order neutral functional differential equations with mixed nonlinearities, Abstr. Appl. Anal. 2011 1–15, 2011.

Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations

Year 2013, Volume: 42 Issue: 2 , 131 - 138 , 01.02.2013
https://izlik.org/JA57DW28JR

Abstract

-

References

  • J. K. Hale, Theory of Functional Differential Equations, Spring-Verlag, New York, 1977. R. P. Agarwal, S. L. Shieh, C. C. Yeh, Oscillation criteria for second order retarded differential equations, Math. Comput. Modelling 26, 1–11, 1997.
  • J. L. Chern, W. Ch. Lian, C. C. Yeh, Oscillation criteria for second order half-linear differential equations with functional arguments, Publ. Math. Debrecen 48, 209–216, 1996. J. Dˇ zurina, I. P. Stavroulakis, Oscillation criteria for second-order delay differential equations, Appl. Math. Comput. 140, 445–453, 2003.
  • T. Kusano, N. Yoshida, Nonoscillation theorems for a class of quasilinear differential equations of second-order, J. Math. Anal. Appl. 189, 115–127, 1995.
  • T. Kusano, Y. Naito, Oscillation and nonoscillation criteria for second order quasilinear differential equations, Acta Math. Hungar. 76, 81–99, 1997.
  • D. D. Mirzov, On the oscillation of solutions of a system of differential equations, Math. Zametki 23, 401–404, 1978.
  • J. Dˇ zurina, D. Hud´ akov´ a, Oscillation of second order neutral delay differential equations, Math. Bohem. 134, 31–38, 2009.
  • B. Bacul´ıkov´ a, D. Lackov´ a, Oscillation criteria for second order retarded differential equations, Studies of the University of Zilina, Mathematical Series. 20, 11–18, 2006.
  • B. Bacul´ıkov´ a, J. Dˇ zurina, Oscillation of third-order neutral differential equations, Math. Comput. Modelling 52, 215–226, 2010.
  • L. Liu, Y. Bai, New oscillation criteria for second-order nonlinear neutral delay differential equations, J. Comput. Math. Appl. 231, 657–663, 2009.
  • R. Xu, F. Meng, Some new oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput. 182, 797–803, 2006.
  • J. G. Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Comput. Math. Appl. 59, 3710–3717, 2010.
  • L. H. Ye, Z. T. Xu, Oscillation criteria for second-order quasilinear neutral delay differential equations, Appl. Math. Comput. 207, 388–396, 2009.
  • Z. Han, T. Li, S. Sun, Y. Sun, Remarks on the paper [Appl. Math. Comput. 207 (2009) 388–396], Appl. Math. Comput. 215, 3998–4007, 2010.
  • Z. Han, T. Li, S. Sun, W. Chen, On the oscillation of second-order neutral delay differential equations, Adv. Differ. Equ. 2010, 1–8, 2010.
  • Z. Han, T. Li, S. Sun, W. Chen, Oscillation criteria for second-order nonlinear neutral delay differential equations, Adv. Differ. Equ. 2010, 1–23, 2010.
  • T. Li, Z. Han, P. Zhao, S. Sun, Oscillation of even-order neutral delay differential equations, Adv. Differ. Equ. 2010, 1–9, 2010.
  • Z. Han, T. Li, S. Sun, W. Chen, Oscillation of second order quasilinear neutral delay differential equations, J. Appl. Math. Comput. 40, 143–152, 2012.
  • T. Li, Z. Han, C. Zhang, S. Sun, On the oscillation of second-order Emden-Fowler neutral differential equations, J. Appl. Math. Comput. 37, 601–610, 2011.
  • S. Sun, T. Li, Z. Han, Y. Sun, Oscillation of second-order neutral functional differential equations with mixed nonlinearities, Abstr. Appl. Anal. 2011 1–15, 2011.
There are 19 citations in total.

Details

Primary Language Turkish
Authors

Tongxing Li This is me

Shurong Sun This is me

Zhenlai Han This is me

Bangxian Han This is me

- - This is me

Yibing Sun This is me

Publication Date February 1, 2013
IZ https://izlik.org/JA57DW28JR
Published in Issue Year 2013 Volume: 42 Issue: 2

Cite

APA Li, T., Sun, S., Han, Z., Han, B., -, -, & Sun, Y. (2013). Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations. Hacettepe Journal of Mathematics and Statistics, 42(2), 131-138. https://izlik.org/JA57DW28JR
AMA 1.Li T, Sun S, Han Z, Han B, -, Sun Y. Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations. Hacettepe Journal of Mathematics and Statistics. 2013;42(2):131-138. https://izlik.org/JA57DW28JR
Chicago Li, Tongxing, Shurong Sun, Zhenlai Han, Bangxian Han, - -, and Yibing Sun. 2013. “Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations”. Hacettepe Journal of Mathematics and Statistics 42 (2): 131-38. https://izlik.org/JA57DW28JR.
EndNote Li T, Sun S, Han Z, Han B, - -, Sun Y (February 1, 2013) Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations. Hacettepe Journal of Mathematics and Statistics 42 2 131–138.
IEEE [1]T. Li, S. Sun, Z. Han, B. Han, - -, and Y. Sun, “Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 2, pp. 131–138, Feb. 2013, [Online]. Available: https://izlik.org/JA57DW28JR
ISNAD Li, Tongxing - Sun, Shurong - Han, Zhenlai - Han, Bangxian - -, - - Sun, Yibing. “Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations”. Hacettepe Journal of Mathematics and Statistics 42/2 (February 1, 2013): 131-138. https://izlik.org/JA57DW28JR.
JAMA 1.Li T, Sun S, Han Z, Han B, - -, Sun Y. Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations. Hacettepe Journal of Mathematics and Statistics. 2013;42:131–138.
MLA Li, Tongxing, et al. “Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 2, Feb. 2013, pp. 131-8, https://izlik.org/JA57DW28JR.
Vancouver 1.Tongxing Li, Shurong Sun, Zhenlai Han, Bangxian Han, - -, Yibing Sun. Oscillation Results for Second-Order Quasi-Linear NeutralDelay Differential Equations. Hacettepe Journal of Mathematics and Statistics [Internet]. 2013 Feb. 1;42(2):131-8. Available from: https://izlik.org/JA57DW28JR