Oscillation of \(3^{\text{rd}}\) order non-canonical delay differential equations of limited neutral coefficient

Volume 37, Issue 4, pp 395--405 https://dx.doi.org/10.22436/jmcs.037.04.04

Publication Date: November 02, 2024 Submission Date: July 26, 2024 Revision Date: September 01, 2024 Accteptance Date: September 10, 2024

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Authors

K‎. ‎ Ramamoorthy - Department of Mathematics‎, ‎College of Engineering and Technology, ‎SRM Institute of Science and Technology, Kattankulathur-603203, Tamil Nadu, India. S‎. ‎K‎. ‎ Thamilvanan - Department of Mathematics‎, ‎College of Engineering and Technology, ‎SRM Institute of Science and Technology, Kattankulathur-603203, Tamil Nadu, India. L. F. Iambor - Department of Mathematics and computer science, ‎University of Oradea, ‎1 University Street‎, ‎410087, ‎Oradea, ‎Romania. Kh. S‎. ‎ Al-Ghafri - University of Technology and Applied Science, ‎P.O‎. ‎BOX 14‎, ‎Ibri 516, ‎Oman. O. Bazighifan - Department of Mathematics‎, ‎Faculty of Education, ‎Seiyun University, ‎Hadhramout, ‎Yemen. - Jadara Research Center, ‎Jadara University, ‎Irbid 21110, Jordan.

Abstract

‎The main aim of this paper is to obtain new criteria for oscillating all solutions of second-order differential equations with distributed deviating arguments and superlinear neutral terms‎. ‎Using the comparative and integral averaging techniques‎, ‎we find new conditions for oscillation that generalize and add to some of the already found results‎. ‎There are examples to show how important the main results are‎.

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Keywords

• Neutral differential equation
• noncanonical‎
• third-order‎
• oscillation

MSC

•  34C10
•  34K11

References

• [1] R. P. Agarwal, M. Bohner, T. Li, C. Zhang, A Philos-type theorem for thirs-order nonlinear retarded dynamic equations, Appl. Math. Comput., 249 (2014), 527–531
  • View Article
  • Google Scholar


• [2] B. Almarri, A. H. Ali, K. S. Al-Ghafri, A. Almutairi, O. Bazighifan, J. Awrejcewicz, Symmetric and Non-Oscillatory Characteristics of the Neutral Differential Equations Solutions Related to p-Laplacian Operators, Symmetry, 14 (2022), 8 pages
  • View Article
  • Google Scholar


• [3] B. Almarri, A. H. Ali, A. M. Lopes, O. Bazighifan, Nonlinear differential equations with distributed delay: some new oscillatory solutions, Mathematics, 10 (2022), 10 pages
  • View Article
  • Google Scholar


• [4] B. Almarri, S. Janaki, V. Ganesan, A. H. Ali, K. Nonlaopon, O. Bazighifan, Novel oscillation theorems and symmetric properties of nonlinear delay differential equations of fourth-order with a middle term, Symmetry, 14 (2022), 1–11
  • View Article
  • Google Scholar


• [5] A. k. Alsharidi, A. Muhib, Oscillation criteria for mixed neutral differential equations, AIMS Math., 9 (2024), 14473–14486
  • View Article
  • MathSciNet
  • Google Scholar


• [6] B. Baculíková, J. Džurina, Oscillation of third-order neutral differential equations, Math. Comput. Model., 52 (2010), 215–225
  • View Article
  • MathSciNet
  • Google Scholar


• [7] A. Bano, A. Dawood, Rida, F. Saira, A. Malik, M. Alkholief, H. Ahmad, M. A. Khan, Z. Ahmad, O. Bazighifan, Enhancing catalytic activity of gold nanoparticles in a standard redox reaction by investigating the impact of AuNPs size, temperature and reductant concentrations, Sci. Rep., 13 (2023), 13 pages
  • View Article
  • Google Scholar


• [8] O. Bazighifan, An approach for studying asymptotic properties of solutions of neutral differential equations, Symmetry, 12 (2020), 8 pages
  • View Article
  • Google Scholar


• [9] O. Bazighifan, T. Abdeljawad, Q. M. Al-Mdallal, Differential equations of even-order with p-Laplacian like operators: qualitative properties of the solutions, Adv. Difference Equ., 2021 (2021), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] O. Bazighifan, A. H. Ali, F. Mofarreh, Y. N. Raffoul, Extended approach to the asymptotic behavior and symmetric solutions of advanced differential equations, Symmetry, 14 (2022), 11 pages
  • View Article
  • Google Scholar


• [11] G. E. Chatzarakis, J. Džurina, I. Jadlovská, Oscillatary properties of third-order neutral delay differential equations with noncannanical operators, Mathematics, 7 (2019), 12 pages
  • View Article
  • Google Scholar


• [12] G. E. Chatzarakis, S. R. Grace, I. Jadlovská, T. Li, E. Tunç, Oscillaiton critaria for third-order Emden-Fowler differential equations with unbounded neutral coefficient, Complelexity, 2019 (2019), 7 pages
  • View Article
  • Google Scholar


• [13] G. E. Chatzarakis, R. Srinivasan, E. Thandapani, Oscillation results for third-order quasilinear Emden-Fowler differential equatione with unbounded neutral coefficients, Tatra Mt. Math. Publ., 80 (2021), 1–14
  • View Article
  • Google Scholar


• [14] A. Columbu, R. Díaz Fuentes, S. Frassu, Uniform-in-time boundedness in a class of local and nonlocal nonlinear attraction-repulsion chemotaxis models with logistics, Nonlinear Anal. Real World Appl., 79 (2024), 14 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] Z. Došlá, P. Liška, Oscillation of third-order nonlinear neutral differential equations, Appl. Math. Lett., 56 (2016), 42–48
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] J. Džurina, E. Thandapani, S. Tamilvanan, Oscillation of solutions to third-order half-linear neutral differential equations, Electron. J. Differ. Equ., 2012 (2012), 9 pages
  • View Article
  • Google Scholar
  • MATH


• [17] J. R. Graef, E. Tunç, S. R. Grace, Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation, Opusc. Math., 37 (2017), 839–852
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] I. Gy˝ori, G. Ladas, Oscillation theory of delay differential equations, The Clarendon Press, Oxford University Press, New York (1991)
  • View Article
  • Google Scholar


• [19] Y. Jiang, C. Jiang, T. Li, Oscillatory behavior of third-order nonlinear neutral delay differential equations, Adv. Difference Equ., 2016 (2016), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] Y.Jiang, T. Li, Asymptotic behavior of a third-order nonlinear neutral delay differential equation, J. Inequal. Appl., 2014 (2014), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] Z. Jiao, I. Jadlovská, T. Li, Global existence in a fully parabolic attraction repulsion chemotaxis system with singular sensitivities and proliferation, J. Differ. Equ., 411 (2024), 227–267
  • View Article
  • MathSciNet
  • Google Scholar


• [22] G. S. Ladde, V. Lakshmikantham, B. G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, New York (1987)
  • View Article
  • Google Scholar


• [23] T. Li, Y. V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [24] T. Li, S. Frassu, G. Viglialoro, Combining effects ensuring boundedness model in an attraction-repulsion chemotaxis model with production and consumption, Z. Angew. Math. Phys., 74 (2023), 21 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] T. Li, Y. V. Rogovchenko, Asymptotic behavior of higher-order quasilinear neutral differential equations, Abstr. Appl. Anal., 2014 (2014), 14 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [26] T. Li, Y. V. Rogovchenko, Asymptotic behavior of an odd-order delay differential equation, Bound. Value Probl., 2014 (2014), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [27] T. Li, Y. V. Rogovchenko, On asymptotic behavior of solutions to higher-order sublinear Emden-Fowler delay differential equations, Appl. Math. Lett., 67 (2017), 53–59
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [28] T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differ. Integral Equ., 34 (2021), 315–336
  • View Article
  • Google Scholar
  • MATH


• [29] T. Li, C. Zhang, G. Xing, Oscillation of thrid-order neutral delay differential equations, Abstr. Appl. Anal., 2012 (2012), 11 pages
  • View Article
  • Google Scholar


• [30] Q. Liu, S. R. Grace, I. Jadlovská, E. Tunç, T. Li, On the asymptotic behavior of noncanonical third-order Emden- Fowler delay differential equations with a superlinear neutral term, Mathematics, 10 (2022), 12 pages
  • View Article
  • Google Scholar


• [31] O. Moaaz, J. Dassios, W. Muhsin, A. Muhib, Osillation theory for nonlinear neutral delay differential equations of third-order, Appl. Sci., 10 (2020), 16 pages
  • View Article
  • Google Scholar


• [32] 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
  • Google Scholar


• [33] O. Moaaz, P. Kumam, O. Bazighifan, On the oscillatory behavior of a class of fourth-order nonlinear differential equation, Symmetry, 12 (2020), 9 pages
  • View Article
  • Google Scholar


• [34] N. Omar, S. Serra-Capizzano, B. Qaraad, F. Alharbi, O. Moaag, E. M. Elabbasy, More effective criteria for testing the oscillation of solutions of third-order differential equations, Axioms, 13 (2024), 11 pages
  • View Article
  • Google Scholar


• [35] S. Padhi, S. Pati, Theory of third-order differential equations, Springer, New Delhi (2014)
  • View Article
  • MathSciNet
  • Google Scholar


• [36] N. Prabaharan, E. Thandapani, E. Tunç, Asymptotic behavior of semi-canonical third-order delay differential equations with a superlinear neutral term, Palest. J. Math., 12 (2023), 473–483
  • View Article
  • Google Scholar


• [37] K. Saranya, V. Piramanantham, E. Thandapani, E. Tunç, Oscillation criteria for third-order semi-canonical differential equations with unbounded neutral coefficients, Stud. Univ. Babe¸s-Bolyai Math., 69 (2024), 115–125
  • View Article
  • Google Scholar


• [38] M. Sohail, U. Nazir, O. Bazighifan, R. A. El-Nabulsi, M. M. Selim, H. Alrabaiah, P. Thounthong, Significant Involvement of Double Diffusion Theories on Viscoelastic Fluid Comprising Variable Thermophysical Properties, Micromachines, 12 (2021), 15 pages
  • View Article
  • Google Scholar


• [39] Y. Sun, Y. Zhao, Q. Xie, Oscillation criteria for third-order neutral differential equations with unbounded neutral coefficients and distributed deviating arguments, Turkish J. Math., 46 (2022), 1099–1112
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [40] E. Thandapani, M. M. A. El-Sheikh, R. Sallam, S. Salem, On the oscillatory behavior of third order differential equations with a sublinear neutral term, Math. Slovaca, 70 (2020), 95–106
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [41] E. Thandapani, T. Li, On the oscillation of third-order quasi-linear neutral functional differential equations, Arch. Math. (Brno), 47 (2011), 181–199
  • View Article
  • Google Scholar
  • MATH


• [42] E. Thandapani, S. Tamilvanan, E. S. Jambulingam, Oscillation of third-order halflinear neutral delay differential equations, Int. J. Pure Appl. Math., 77 (2012), 359–368
  • View Article
  • Google Scholar


• [43] E. Tunç, S. R. Grace, Oscillatory behavior of solutions to third-order nonlinear differential equations with a superlinear neutral term, Electron. J. Differ. Equ., 2020 (2020), 11 pages
  • View Article
  • Google Scholar
  • MATH


• [44] E. Tunç, S. ¸Sahin, J. R. Graef, S. Pinelas, New oscillation criteria for third-order differential equations with bounded and unbounded neutral coefficients, Electron. J. Qual. Theory Differ. Equ., 2021 (2021), 13 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [45] K. S. Vidhyaa, J. R. Graef, E. Thandapani, New oscillation results for third-order half-linear neutral differential equations, Mathematics, 8 (2020), 9 pages
  • View Article
  • Google Scholar