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Year 2020, Volume: 49 Issue: 2, 766 - 776, 02.04.2020
https://doi.org/10.15672/hujms.471023

Abstract

References

  • [1] R.P. Agarwal, S.R. Grace, and D. O’Regan, Oscillation theory for second order linear, half-linear, superlinear and sublinear dynamic equations, Springer Science & Business Media, 2002.
  • [2] R.P. Agarwal, S.R. Grace, and P.J.Y. Wong, Oscillation theorems for certain higher order nonlinear functional differential equations, Appl. Anal. Discr. Math. 2, 1–30, 2008.
  • [3] R.P. Agarwal, M. Bohner, T. Li, and C. Zhang, A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput. 225, 787–794, 2013.
  • [4] R.P. Agarwal, M. Bohner, T. Li, and C. Zhang, Oscillation of second order differential equations with a sublinear neutral term, Carpathian J. Math. 30 (1), 1–6, 2014.
  • [5] J.G. Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Comput. Math. Appl. 59, 3710 – 3717, 2010.
  • [6] S.R. Grace and B.S. Lalli, Oscillation of nonlinear second order neutral differential equations, Rat. Math. 3, 77 – 84, 1987.
  • [7] S.R. Grace, J.R. Graef, and M.A. El-Beltagy, On the oscillation of third order neutral delay dynamic equations on time scales, Comput. Math. Appl. 63 (4), 775–782, 2012.
  • [8] S.R. Grace and I. Jadlovská, Oscillation Criteria for second-order neutral damped differential equations with delay argument, in: Dynamical Systems - Analytical and Computational Techniques, InTech, 2017.
  • [9] S.R. Grace,Oscillatory behavior of second-order nonlinear differential equations with a nonpositive neutral term, Mediterr. J. Math. 14 (6), Art. 229, 2017.
  • [10] G.H. Hardy, I.E. Littlewood, and G. Polya, Inequalities, University Press, Cambridge, 1959.
  • [11] B. Karpuz, O. Ocalan, and S. Ozturk, Comparison theorems on the oscillation and asymptotic behaviour of higher-order neutral differential equations, Glasgow Math. J. 52 (1), 107–114, 2010.
  • [12] I.T. Kiguradze, On the oscillation of solutions of the Eq. $d^mu/dt^m+a(t)|u|^n {\rm sgn}u = 0$, Mat. Sb. 65, 172–187, 1964 (in Russian).
  • [13] T. Li, Z. Han, C. Zhang, and H. Li, Oscillation criteria for second-order superlinear neutral differential equations, Abstr. Appl. Anal. 2011, 2011.
  • [14] T. Li, Yu.V. Rogovchenko, and C. Zhang, Oscillation results for second-order nonlinear neutral differential equations, Adv. Differ. Equ. 2013, 1 – 13, 2013.
  • [15] Q. Li, R. Wang, F. Chen, and T. Li , Oscillation of second-order nonlinear delay differential equations with nonpositive neutral coefficients, Adv. Differ. Equ. 2015, 1–15, 2015.
  • [16] Ch. G. Philos, A new criterion for the oscillatory and asymptotic behavior of delay differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Mat. 39 (1), 61–64, 1981.
  • [17] H. Qin, N. Shang, and Y. Lu, A note on oscillation criteria of second order nonlinear neutral delay differential equations, Comput. Math. Appl. 56, 2987–299, 2008.
  • [18] V. Staikos and I. Stavroulakis, Bounded oscillations under the effect of retardations for differential equations of arbitrary order, P. Roy. Soc. Edinb. 77 (1), 129–136, 1977.
  • [19] H. Wu, L. Erbe, and A. Peterson, Oscillation of solution to second-order half-linear delay dynamic equations on time scales, Electron. J. Differ. Eq. 2016 (71), 1–15, 2016.
  • [20] J.S.W. Wong, Necessary and sufficient conditions for oscillation of second order neutral differential equations, J. Math. Anal. Appl. 252, 342–352, 2000.
  • [21] Q. Yang, l. Yang, and S. Zhu, Interval criteria for oscillation of second-order nonlinear neutral differential equations, Comput. Math. Appl. 46 (5), 903–918, 2003.

Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term

Year 2020, Volume: 49 Issue: 2, 766 - 776, 02.04.2020
https://doi.org/10.15672/hujms.471023

Abstract

We study the oscillation problem for solutions of a class of $n$-th order nonlinear delay differential equations with nonpositive neutral terms. The obtained results improve and correlate many of the known oscillation criteria in the literature for neutral and non-neutral equations.

References

  • [1] R.P. Agarwal, S.R. Grace, and D. O’Regan, Oscillation theory for second order linear, half-linear, superlinear and sublinear dynamic equations, Springer Science & Business Media, 2002.
  • [2] R.P. Agarwal, S.R. Grace, and P.J.Y. Wong, Oscillation theorems for certain higher order nonlinear functional differential equations, Appl. Anal. Discr. Math. 2, 1–30, 2008.
  • [3] R.P. Agarwal, M. Bohner, T. Li, and C. Zhang, A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput. 225, 787–794, 2013.
  • [4] R.P. Agarwal, M. Bohner, T. Li, and C. Zhang, Oscillation of second order differential equations with a sublinear neutral term, Carpathian J. Math. 30 (1), 1–6, 2014.
  • [5] J.G. Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Comput. Math. Appl. 59, 3710 – 3717, 2010.
  • [6] S.R. Grace and B.S. Lalli, Oscillation of nonlinear second order neutral differential equations, Rat. Math. 3, 77 – 84, 1987.
  • [7] S.R. Grace, J.R. Graef, and M.A. El-Beltagy, On the oscillation of third order neutral delay dynamic equations on time scales, Comput. Math. Appl. 63 (4), 775–782, 2012.
  • [8] S.R. Grace and I. Jadlovská, Oscillation Criteria for second-order neutral damped differential equations with delay argument, in: Dynamical Systems - Analytical and Computational Techniques, InTech, 2017.
  • [9] S.R. Grace,Oscillatory behavior of second-order nonlinear differential equations with a nonpositive neutral term, Mediterr. J. Math. 14 (6), Art. 229, 2017.
  • [10] G.H. Hardy, I.E. Littlewood, and G. Polya, Inequalities, University Press, Cambridge, 1959.
  • [11] B. Karpuz, O. Ocalan, and S. Ozturk, Comparison theorems on the oscillation and asymptotic behaviour of higher-order neutral differential equations, Glasgow Math. J. 52 (1), 107–114, 2010.
  • [12] I.T. Kiguradze, On the oscillation of solutions of the Eq. $d^mu/dt^m+a(t)|u|^n {\rm sgn}u = 0$, Mat. Sb. 65, 172–187, 1964 (in Russian).
  • [13] T. Li, Z. Han, C. Zhang, and H. Li, Oscillation criteria for second-order superlinear neutral differential equations, Abstr. Appl. Anal. 2011, 2011.
  • [14] T. Li, Yu.V. Rogovchenko, and C. Zhang, Oscillation results for second-order nonlinear neutral differential equations, Adv. Differ. Equ. 2013, 1 – 13, 2013.
  • [15] Q. Li, R. Wang, F. Chen, and T. Li , Oscillation of second-order nonlinear delay differential equations with nonpositive neutral coefficients, Adv. Differ. Equ. 2015, 1–15, 2015.
  • [16] Ch. G. Philos, A new criterion for the oscillatory and asymptotic behavior of delay differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Mat. 39 (1), 61–64, 1981.
  • [17] H. Qin, N. Shang, and Y. Lu, A note on oscillation criteria of second order nonlinear neutral delay differential equations, Comput. Math. Appl. 56, 2987–299, 2008.
  • [18] V. Staikos and I. Stavroulakis, Bounded oscillations under the effect of retardations for differential equations of arbitrary order, P. Roy. Soc. Edinb. 77 (1), 129–136, 1977.
  • [19] H. Wu, L. Erbe, and A. Peterson, Oscillation of solution to second-order half-linear delay dynamic equations on time scales, Electron. J. Differ. Eq. 2016 (71), 1–15, 2016.
  • [20] J.S.W. Wong, Necessary and sufficient conditions for oscillation of second order neutral differential equations, J. Math. Anal. Appl. 252, 342–352, 2000.
  • [21] Q. Yang, l. Yang, and S. Zhu, Interval criteria for oscillation of second-order nonlinear neutral differential equations, Comput. Math. Appl. 46 (5), 903–918, 2003.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Said R. Grace 0000-0001-8783-5227

İrena Jadlovska 0000-0003-4649-5611

Zafer Ağacık 0000-0001-8446-1223

Publication Date April 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 2

Cite

APA Grace, S. R., Jadlovska, İ., & Ağacık, Z. (2020). Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term. Hacettepe Journal of Mathematics and Statistics, 49(2), 766-776. https://doi.org/10.15672/hujms.471023
AMA Grace SR, Jadlovska İ, Ağacık Z. Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term. Hacettepe Journal of Mathematics and Statistics. April 2020;49(2):766-776. doi:10.15672/hujms.471023
Chicago Grace, Said R., İrena Jadlovska, and Zafer Ağacık. “Oscillatory Behavior of $n$-Th Order Nonlinear Delay Differential Equations With a Nonpositive Neutral Term”. Hacettepe Journal of Mathematics and Statistics 49, no. 2 (April 2020): 766-76. https://doi.org/10.15672/hujms.471023.
EndNote Grace SR, Jadlovska İ, Ağacık Z (April 1, 2020) Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term. Hacettepe Journal of Mathematics and Statistics 49 2 766–776.
IEEE S. R. Grace, İ. Jadlovska, and Z. Ağacık, “Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, pp. 766–776, 2020, doi: 10.15672/hujms.471023.
ISNAD Grace, Said R. et al. “Oscillatory Behavior of $n$-Th Order Nonlinear Delay Differential Equations With a Nonpositive Neutral Term”. Hacettepe Journal of Mathematics and Statistics 49/2 (April 2020), 766-776. https://doi.org/10.15672/hujms.471023.
JAMA Grace SR, Jadlovska İ, Ağacık Z. Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term. Hacettepe Journal of Mathematics and Statistics. 2020;49:766–776.
MLA Grace, Said R. et al. “Oscillatory Behavior of $n$-Th Order Nonlinear Delay Differential Equations With a Nonpositive Neutral Term”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, 2020, pp. 766-7, doi:10.15672/hujms.471023.
Vancouver Grace SR, Jadlovska İ, Ağacık Z. Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term. Hacettepe Journal of Mathematics and Statistics. 2020;49(2):766-7.