Yıl 2020, Cilt 49 , Sayı 2, Sayfalar 766 - 776 2020-04-02

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

Said R. GRACE [1] , İrena JADLOVSKA [2] , Zafer AĞACIK [3]


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.
Oscillation, neutral term, second order differential equation
  • [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.
Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0001-8783-5227
Yazar: Said R. GRACE
Kurum: Cairo University
Ülke: Egypt


Orcid: 0000-0003-4649-5611
Yazar: İrena JADLOVSKA
Kurum: Technical University of Košice
Ülke: Slovakia


Orcid: 0000-0001-8446-1223
Yazar: Zafer AĞACIK (Sorumlu Yazar)
Kurum: American University of the Middle East
Ülke: Kuwait


Tarihler

Yayımlanma Tarihi : 2 Nisan 2020

Bibtex @araştırma makalesi { hujms471023, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {766 - 776}, doi = {10.15672/hujms.471023}, title = {Oscillatory behavior of \$n\$-th order nonlinear delay differential equations with a nonpositive neutral term}, key = {cite}, author = {GRACE, Said R. and JADLOVSKA, İrena and AĞACIK, Zafer} }
APA GRACE, S , JADLOVSKA, İ , AĞACIK, 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 . DOI: 10.15672/hujms.471023
MLA GRACE, S , JADLOVSKA, İ , AĞACIK, Z . "Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 766-776 <https://dergipark.org.tr/tr/pub/hujms/issue/53568/471023>
Chicago GRACE, S , JADLOVSKA, İ , AĞACIK, Z . "Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 766-776
RIS TY - JOUR T1 - Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term AU - Said R. GRACE , İrena JADLOVSKA , Zafer AĞACIK Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.471023 DO - 10.15672/hujms.471023 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 766 EP - 776 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.471023 UR - https://doi.org/10.15672/hujms.471023 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term %A Said R. GRACE , İrena JADLOVSKA , Zafer AĞACIK %T Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.471023 %U 10.15672/hujms.471023
ISNAD GRACE, Said R. , JADLOVSKA, İrena , AĞACIK, Zafer . "Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 766-776 . https://doi.org/10.15672/hujms.471023
AMA GRACE S , JADLOVSKA İ , AĞACIK 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): 766-776.
Vancouver GRACE S , JADLOVSKA İ , AĞACIK 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): 776-766.