New oscillation results for higher order nonlinear differential equations with a nonlinear neutral terms

Volume 28, Issue 3, pp 294--305 http://dx.doi.org/10.22436/jmcs.028.03.07

Publication Date: June 26, 2022 Submission Date: January 01, 2022 Revision Date: February 28, 2022 Accteptance Date: May 21, 2022

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Authors

J. Alzabut - Department of Mathematics and General Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia. - Department of Industrial Engineering, OSTIM Technical University, 06374 Ankara, Turkiye. S. R. Grace - Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt. G. N. Chhatria - Department of Mathematics, Sambalpur University, Sambalpur 768019, India.

Abstract

The paper deals with the oscillation of higher order nonlinear differential equations with a nonlinear neutral term. The main results are proved via utilizing an integral criterion as well as a comparison theorem with first-order delay differential equation whose oscillatory properties are known. The proposed theorems improve, extend, and simplify existing ones in the literature. The results are associated with four numerical examples.

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Keywords

• Oscillation
• asymptotic behavior
• neutral differential equation
• comparison method

MSC

•  34K11

References

• [1] H. A. Abd El-Hamid, H. M. Rezk, A. M. Ahmed, G. AlNemer, M. Zakarya, H. A. El Saify, Some dynamic Hilbert-type inequalities for two variables on time scales, J. Inequal. Appl., 2021 (2021), 21 pages
  • View Article
  • MathSciNet


• [2] R. P. Agarwal, M. Bohner, T. X. Li, C. H. Zhang, Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math., 30 (2014), 1--6
  • View Article
  • MathSciNet


• [3] R. P. Agarwal, S. R. Grace, The oscillation of higher-order differential equations with deviating arguments, Comput. Math. Appl., 38 (1999), 185--199
  • View Article
  • MathSciNet


• [4] R. P. Agarwal, S. R. Grace, D. O’Regan, Oscillation criteria for certain nth order differential equations with deviating arguments, J. Math. Anal. Appl., 262 (2001), 601--622
  • View Article


• [5] R. P. Agarwal, S. R. Grace, D. O’Regan, The oscillation of certain higher-order functional differential equations, Math. Comput. Modelling, 37 (2003), 705--728
  • View Article
  • MathSciNet


• [6] R. P. Agarwal, S. R. Grace, D. O’Regan, Oscillation of certain fourth order functional differential equations, Ukrainian Math. J., 59 (2007), 315--342
  • View Article
  • MathSciNet


• [7] R. P. Agarwal, S. R. Grace, D. O’Regan, Oscillation Theory for Difference and Functional Difference Equations, Springer Science & Business Media, Berlin/Heidelberg (2013)
  • View Article


• [8] P. Agarwal, A.-A. Hyder, M. Zakarya, Well-posedness of Stochastic modified Kawahara equation, Adv. Difference Equ., 2020 (2020), 10 pages
  • View Article
  • MathSciNet


• [9] G. AlNemer, M. Zakarya, H. A. Abd El-Hamid, M. R. Kenawy, H. M. Rezk, Dynamic Hardy-type inequalities with non-conjugate parameters, Alex. Eng. J., 59 (2020), 4523--4532
  • View Article


• [10] B. Baculíková, J. Džurina, T. X. Li, Oscillation results for even-order quasilinear neutral functional differential equations, Electron. J. Differ. Equ., 2011 (2011), 9 pages
  • View Article
  • MathSciNet


• [11] M. Bartušek, M. Cecchi, Z. Došlá, M. Marini, Asymptotics for higher order differential equations with a middle term, J. Math. Anal. Appl., 388 (2012), 1130--1140
  • View Article
  • MathSciNet


• [12] O. Bazighifan, R. A. El-Nabulsi, Different techniques for studying oscillatory behavior of solution of differential equations, Rocky Mountain J. Math., 51 (2021), 77--86
  • View Article
  • MathSciNet


• [13] O. Bazighifan, O. Moaaz, R. A. El-Nabulsi, A. Muhib, Some new oscillation results for fourth-order neutral differential equations with delay argument, Symmetry, 12 (2020), 10 pages
  • View Article


• [14] C. Cesarano, O. Moaaz, B. Qaraad, N. A. Alshehri, S. K. Elagan, M. Zakarya, New results for oscillation of solutions of odd-order neutral differential equations, Symmetry, 13 (2021), 12 pages
  • View Article


• [15] R. A. El-Nabulsi, A generalized nonlinear oscillator from non-standard degenerate lagrangians and its consequent hamiltonian formalism, Proc. Nat. Acad. Sci. India Sect. A, 84 (2014), 563--569
  • View Article
  • MathSciNet


• [16] R. A. El-Nabulsi, Non-standard power-law Lagrangians in classical and quantum dynamics, Appl. Math. Lett., 43 (2015), 120--127
  • View Article
  • MathSciNet


• [17] R. A. El-Nabulsi, Complex backward-forward derivative operator in non-local-in-time Lagrangians mechanics, Qual. Theory Dyn. Syst., 16 (2017), 223--234
  • View Article
  • MathSciNet


• [18] R. A. El-Nabulsi, Dynamics of pulsatile flows through microtubes from nonlocality, Mech. Res. Commun., 86 (2017), 18--26
  • View Article


• [19] R. A. El-Nabulsi, Nonlocal-in-time kinetic energy in nonconservative fractional systems, disordered dynamics, jerk and snap and oscillatory motions in the rotating fluid tube, Int. J. Non-Linear Mechanics, 93 (2017), 65--81
  • View Article


• [20] R. A. El-Nabulsi, O. Moaaz, O. Bazighifan, New results for oscillatory behavior of fourth-order differential equations, Symmetry, 12 (2020), 12 pages
  • View Article


• [21] H. A. Ghany, Abd-Allah Hyder, M. Zakarya, Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives, Chin. Phys. B, 29 (2020), 1--8
  • View Article


• [22] H. A. Ghany, M. Zakarya, Exact solitary wave solutions for wick-type stochastic (2 + 1)-dimensional coupled KdV equations, J. Comput. Anal. Appl., 29 (2020), 617--633
  • View Article


• [23] S. R. Grace, J. Džurina, I. Jadlovská, T. X. Li, An improved approach for studying oscillation of second-order neutral delay differential equations, J. Inequal. Appl., 2018 (2018), 13 pages
  • View Article
  • MathSciNet


• [24] S. R. Grace, J. R. Graef, Oscillatory behavior of second order nonlinear differential equations with a sublinear neutral term, Math. Model. Anal., 23 (2018), 217--226
  • View Article
  • MathSciNet


• [25] S. R. Grace, J. R. Graef, M. A. El-Beltagy, On the oscillation of third order delay dynamic equations on time scales, Comput. Math. Appl., 63 (2012), 775--782
  • View Article
  • MathSciNet


• [26] S. R. Grace, J. R. Graef, I. Jadlovska, Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms, Math. Slovaca, 69 (2019), 1117--1126
  • View Article
  • MathSciNet


• [27] S. R. Grace, J. R. Graef, E. Tunc, Oscillatory behaviour of second order damped neutral differential equations with distributed deviating arguments, Miskolc Math. Notes, 18 (2017), 759--769
  • View Article


• [28] J. Graef, S. Grace, E. Tunc, Oscillation criteria for even-order differential equations with unbounded neutral coefficients and distributed deviating arguments, Funct. Differ. Equ., 25 (2018), 143--153
  • View Article
  • MathSciNet


• [29] J. R. Graef, S. R. Grace, E. Tunc, Oscillatory behaviour of even-order nonlinear differential equations with a sublinear neutral term, Opuscula Math., 39 (2019), 39--47
  • View Article


• [30] S. R. Grace, I. Jadlovska, Oscillatory behavior of odd order nonlinear differential equations with a nonpositive neutral term, Dyn. Syst. Appl., 27 (2018), 125--136
  • View Article


• [31] J. R. Graef, M. K. Grammatikopoulos, P. W. Spikes, On the asymptotic behavior of solutions of a second order nonlinear neutral delay differential equation, J. Math. Anal. Appl., 156 (1991), 23--39
  • View Article
  • MathSciNet


• [32] J. R. Graef, C. Qian, B. Yang, A three point boundary value problem for nonlinear fourth order differential equations, J. Math. Anal. Appl., 287 (2003), 217--233
  • View Article
  • MathSciNet


• [33] J. R. Graef, P. W. Spikes, On the oscillation of an nth-order nonlinear neutral delay differential equation, J. Comput. Appl. Math., 41 (1992), 35--40
  • View Article


• [34] G. Gupta, M. Massoudi, Flow of a generalized second grade fluid between heated plates, Acta Mechanica, 99 (1993), 21--33
  • View Article


• [35] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge University Press, Cambridge (1934)
  • Google Scholar


• [36] T. Hayat, Y. Wang, A. M. Siddiqui, K. Hutter, S. Asghar, Peristaltic transport of a third-order fluid in a circular cylindrical tube, Math. Models Methods Appl. Sci., 12 (2002), 1691--1706
  • View Article
  • MathSciNet


• [37] D. B. Ingham, B. Yan, Fluid flow induced by a small amplitude harmonically oscillating cascade, Acta Mechanica, 91 (1992), 27--46
  • View Article


• [38] K. Kamo, H. Usami, Nonlinear oscillations of fourth Order quasilinear ordinary Differential equations, Acta Math. Hungar., 132 (2011), 207--222
  • View Article
  • MathSciNet


• [39] I. T. Kiguradze, On the oscillatory character of solutions of the equation $dmu/dtm + a(t)|u| n \;sign\; u = 0$, Mat. Sb. (N.S.), 65 (1964), 172--187
  • View Article
  • MathSciNet


• [40] M. M. Kipnis, D. A. Komissarova, A note on explicit stability conditions for autonomous higher order difference equations, J. Difference Equ. Appl., 13 (2007), 457--461
  • View Article
  • MathSciNet


• [41] Y. Kitamura, T. Kusano, Oscillation of first order nonlinear differential equations with deviating arguments, Proc. Amer. Math. Soc., 78 (1980), 64--68
  • View Article
  • MathSciNet


• [42] R. G. Koplatadze, T. A. Chanturiya, Oscillating and monotone solutions of first-order differential equations with deviating argument, (Russian), Differentsial’nye Uravneniya, 18 (1982), 1463--1465
  • View Article
  • MathSciNet


• [43] W. N. Li, Oscillation of higher order delay differential equations of neutral type, Georgian Math. J., 7 (2000), 347--353
  • View Article
  • MathSciNet


• [44] T.-X. Li, Y. V. Rogovchenko, Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett., 61 (2016), 35--41
  • View Article
  • MathSciNet


• [45] T. X. Li, Y. V. Rogovchenko, Oscillation criteria for second–order superlinear Emden–Fowler neutral differential equations, Monatsh. Math., 184 (2017), 489--500
  • View Article
  • MathSciNet


• [46] O. Moaaz, R. A. El-Nabulsi, O. Bazighifan, Behavior of non-oscillatory solutions of fourth-order neutral differential equations, Symmetry, 12 (2020), 12 pages
  • View Article


• [47] O. Moaaz, R. A. El-Nabulsi, O. Bazighifan, Oscillatory behavior of fourth-order differential equations with neutral delay, Symmetry, 12 (2020), 8 pages
  • View Article


• [48] O. Moaaz, R. A. El-Nabulsi, O. Bazighifan, A. Muhib, New comparison theorems for the even-order neutral delay differential equation, Symmetry, 12 (2020), 11 pages
  • View Article


• [49] O. Moaaz, R. A. El-Nabulsi, A. Muhib, S. K. Elagan, M. Zakarya, New improved results for oscillation of fourth-order neutral differential equations, Mathematics, 9 (2021), 12 pages
  • View Article


• [50] M. Naito, F. Wu, A note on the existence and asymptotic behavior of nonoscillatory solutions of fourth order quasilinear differential equations, Acta Math. Hungar., 102 (2004), 177--202
  • View Article


• [51] N. Parhi, A. K. Tripathy, On oscillatory fourth order nonlinear neutral differential equations-I, Math. Slovaca, 54 (2004), 389--410
  • View Article
  • MathSciNet


• [52] C. G. Philos, On the existence of nonoscillatory solutions tending to zero at $\infty$ for differential equations with positive delays, Arch. Math. (Basel), 36 (1981), 168--178
  • View Article
  • MathSciNet


• [53] H. M. Rezk, G. AlNemer, H. A. Abd El-Hamid, A. H Abdel-Aty, K. S. Nisar, M. Zakarya, Hilbert-type inequalities for time scale nabla calculus, Adv. Difference Equ., 2020 (2020), 21 pages
  • View Article
  • MathSciNet


• [54] Y. Sun, Z. Han, S. Sun, C. Zhang, Oscillation criteria for even order nonlinear neutral differential equations, Electron. J. Qual. Theory Differ. Equ., 2012 (2012), 12 pages
  • View Article
  • MathSciNet


• [55] P. G. Wang, W. Y. Shi, Oscillatory theorems of a class of even-order neutral equations, Appl. Math. Lett., 16 (2003), 1011--1018
  • View Article
  • MathSciNet


• [56] Y. Wang, W. Wu, Unsteady flow of a fourth-grade fluid due to an oscillating plate, Int. J. Non-Linear Mechanics, 42 (2007), 432--441
  • View Article


• [57] W. M. Xiong, G. G. Yue, Almost periodic solutions for a class of fourth-order nonlinear differential equations with a deviating argument, Comput. Math. Appl., 60 (2010), 1184--1190
  • View Article
  • MathSciNet


• [58] J. L. Yao, F. W. Meng, Asymptotic behavior of solutions of certain higher order nonlinear difference equation, J. Comput. Appl. Math., 205 (2007), 640--650
  • View Article


• [59] A. Zafer, Oscillation criteria for even order neutral differential equations, Appl. Math. Lett., 11 (1998), 21--25
  • View Article
  • MathSciNet


• [60] M. Zakarya, Hypercomplex Systems and Non-Gaussian Stochastic solutions of $\chi$- wick type $(3+1)$-dimensional modified Benjamin-Bona-Mahony Equation, Thermal Science, 24 (2020), 209--223
  • View Article
  • Google Scholar


• [61] Q. Zhang, J. Yan, L. Gao, Oscillation behaviour of even-order nonlinear neutral differential equations with variable coefficients, Comput. Math. Appl., 59 (2010), 426--430
  • View Article
  • Google Scholar