Research article Special Issues

Oscillation behavior for neutral delay differential equations of second-order


  • Received: 20 February 2021 Accepted: 29 April 2021 Published: 20 May 2021
  • In this paper, new criteria for oscillation of neutral delay differential equations of second-order are presented. One objective of this study is to complement and extend some well-known related results in the literature. To support our main results, we give illustrating examples.

    Citation: Osama Moaaz, Ali Muhib, Waed Muhsin, Belgees Qaraad, Hijaz Ahmad, Shao-Wen Yao. Oscillation behavior for neutral delay differential equations of second-order[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 4390-4401. doi: 10.3934/mbe.2021221

    Related Papers:

  • In this paper, new criteria for oscillation of neutral delay differential equations of second-order are presented. One objective of this study is to complement and extend some well-known related results in the literature. To support our main results, we give illustrating examples.



    加载中


    [1] B. Baculikova, J. Dzurina, Oscillation theorems for second order nonlinear neutral differential equations, Comput. Math. Appl., 62 (2011), 4472–4478. doi: 10.1016/j.camwa.2011.10.024
    [2] J. G. Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Comput. Math. Appl., 59 (2010), 3710–3717. doi: 10.1016/j.camwa.2010.04.004
    [3] S. R. Grace, B. S. Lalli, Oscillation of nonlinear second order neutral delay differential equations, Rad. Math., 3 (1987), 77–84.
    [4] S. R. Grace, J. Dzurina, I. Jadlovska, T. Li, An improved approach for studying oscillation of second-order neutral delay differential equations, J. Ineq. Appl., 2018 (2008), 193.
    [5] B. Baculikova, J. Dzurina, Oscillation theorems for second order neutral differential equations, Comput. Math. Appl., 61 (2011), 94–99. doi: 10.1016/j.camwa.2010.10.035
    [6] O. Moaaz, New criteria for oscillation of nonlinear neutral differential equations, Adv. Differ. Equations, (2019), 484.
    [7] R. P. Agarwal, Ch. Zhang, T. Li, Some remarks on oscillation of second order neutral differential equations, Appl. Math. Comput., 274, (2016), 178–181.
    [8] M. Bohner, S. R. Grace, I. Jadlovska, Oscillation criteria for second-order neutral delay differential equations, Electron. J. Qual. Theory Differ. Equations, 60 (2017).
    [9] O. Moaaz, E. M. Elabbasy, B. Qaraad, An improved approach for studying oscillation of generalized Emden-Fowler neutral differential equation, J. Ineq. Appl., 69 (2020).
    [10] O. Moaaz, A. Muhib, S. Owyed, E. E. Mahmoud, A. Abdelnaser, Second-order neutral differential equations: improved criteria for testing the oscillation, J. Math., 2021.
    [11] O. Moaaz, M. Anis, D. Baleanu, A. Muhib, More effective criteria for oscillation of second-order differential equations with neutral arguments, Mathematics, 8 (2020), 986. doi: 10.3390/math8060986
    [12] B. Baculikova, J. Dzurina, T. Li, Oscillation results for even-order quasilinear neutral functional differential equations, Electron. J. Differ. Equations, 2011 (2011), 1–9.
    [13] R. P. Agarwal, M. Bohner, T. Li, C. Zhang, A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput., 225 (2013), 787–794.
    [14] B. Baculikova, J. Dzurina, Oscillation theorems for higher order neutral differential equations, Appl. Math. Comput., 219 (2012), 3769–3778.
    [15] O. Moaaz, E. M. Elabbasy, E. Shaaban, Oscillation criteria for a class of third order damped differential equations, Arab J. Math. Sci., 24, (2018), 16–30.
    [16] O. Moaaz, S. Furuichi, A. Muhib, New comparison theorems for the nth order neutral differential equations with delay inequalities, Mathematics, 8 (2020), 454. doi: 10.3390/math8030454
    [17] L. Liu, Y. Bai, New oscillation criteria for second-order nonlinear neutral delay differential equations, J. Comput. Appl. Math., 231 (2009), 657–663. doi: 10.1016/j.cam.2009.04.009
    [18] R. Xu, F. Meng, Some new oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput., 182 (2006), 797–803.
    [19] R. Xu, F. Meng, Oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput., 192 (2007), 216–222.
    [20] Z. Han, T. Li, S. Sun, W. Chen, On the oscillation of second-order neutral delay differential equations, Adv. Differ. Equations, (2010), 1–8.
    [21] Z. Han, T. Li, S. Sun, W. Chen, Oscillation criteria for second-order nonlinear neutral delay differential equations, Adv. Differ. Equations, (2010), 1–23.
    [22] T. Li, Z. Han, P. Zhao, S. Sun, Oscillation of even-order neutral delay differential equations, Adv. Differ. Equations, (2010), 1–9.
    [23] G. Ladde, V. Lakshmikantham, B. Zhang, Oscillation theory of differential equations with deviating arguments, Marcel Dekker, NewYork, 1987.
    [24] H. Liu, F. Meng, P. Liu, Oscillation and asymptotic analysis on a new generalized Emden–Fowler equation, Appl. Math. Comput., 219 (2012), 2739–2748.
    [25] C. Philos, On the existence of nonoscillatory solutions tending to zero at $\infty $for differential equations with positive delay, Arch. Math., 36 (1981), 168–178. doi: 10.1007/BF01223686
    [26] Y. Wu, Y. Yu, J. Zhang, J. Xiao, Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type, Appl. Math. Comput., 210 (2012), 2739–2748.
    [27] C. Zhang, R. P. Agarwal, M. Bohner, T. Li, New results for oscillatory behavior of even-order half-linear delay differential equations, Appl. Math. Lett., 26 (2013), 179–183. doi: 10.1016/j.aml.2012.08.004
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2485) PDF downloads(127) Cited by(1)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog