The aim of this work is to study some oscillation behavior of solutions of a class of third-order neutral differential equations with multi delays. We present new oscillation criteria that complete and simplify some previous results. We also provide an example to clarify the significance of our results.
Citation: Maryam AlKandari. Nonlinear differential equations with neutral term: Asymptotic behavior of solutions[J]. AIMS Mathematics, 2024, 9(12): 33649-33661. doi: 10.3934/math.20241606
The aim of this work is to study some oscillation behavior of solutions of a class of third-order neutral differential equations with multi delays. We present new oscillation criteria that complete and simplify some previous results. We also provide an example to clarify the significance of our results.
[1] | R. P. Agarwal, O. Bazighifan, M. A. Ragusa, Nonlinear neutral delay differential equations of fourth-order: Oscillation of solutions, Entropy, 23 (2021), 1–10. http://dx.doi.org/10.3390/e23020129 doi: 10.3390/e23020129 |
[2] | G. E. Chatzarakis, J. Dzurina, I. Jadlovska, Oscillatary properties of third-order neutral delay differential equations with noncannanical operators, Mathematics, 7 (2019), 1–12. http://dx.doi.org/10.3390/math7121177 doi: 10.3390/math7121177 |
[3] | T. Jin, F. Li, H. Peng, B. Li, D. Jiang, Uncertain barrier swaption pricing problem based on the fractional differential equation in Caputo sense, Soft Comput., 27 (2023). http://dx.doi.org/10.1007/s00500-023-08153-5 |
[4] | P. Cai, Y. Zhang, T. Jin, Y. Tod, S. Gao, Self-Adaptive Forensic-Based investigation algorithm with dynamic population for solving constraint optimization problems, Int. J. Comput. Intell. Syst., 17 (2024). http://dx.doi.org/10.1007/s44196-023-00396-2 |
[5] | B. Baculikova, J. Dzurina, Oscillation of third-order neutral differential equations, Math. Comput. Model., 52 (2010), 215–226. http://dx.doi.org/10.1016/j.mcm.2010.02.011 doi: 10.1016/j.mcm.2010.02.011 |
[6] | S. R. Grace, J. Dzurina, I. Jadlovska, T. Li, On the oscillation of fourth-order delay differential equations, Adv. Differnce Equ., 2019 (2019), 1–15. http://dx.doi.org/10.1186/s13662-019-2060-1 doi: 10.1186/s13662-019-2060-1 |
[7] | G. S. Ladde, V. Lakshmikantham, B. G. Zhang, Oscillation theory of differential equations with deviating arguments, M. Dekker, 1987. |
[8] | Z. Dosla, P. Liska, Comparison theorems for third-order neutral differential equations, Electron. J. Differential Equations, 13 (2016), 1–11. |
[9] | Z. Dosla, P. Liska, Oscillation of third-order neutral differetial equation, Appl. Math. Lett., 56 (2016), 42–48. http://dx.doi.org/10.1016/j.aml.2015.12.010 doi: 10.1016/j.aml.2015.12.010 |
[10] | I. Gyori, G. Ladas, Oscillation theory for delay differential equations with applications, Oxford: Clarendon Press, 1991. http://dx.doi.org/10.1093/oso/9780198535829.001.0001 |
[11] | J. K. Hale, Theory of functional differential equations, New York: Springer, 1977. |
[12] | N. Kilinc Gecer, P. Temtek, Oscillation criteria for fourth-order differential equations, Erciyes Üniv. Fen Biliml. Enstitüsü Fen Bilimleri Derg., 38 (2022), 109–116. |
[13] | A. A. El-Gaber, M. M. A. El-sheikh, Oscillation of fourth-order neutral differential equations with distributed deviating arguments, J. Math. Computer Sci., 28 (2023), 60–71. http://dx.doi.org/10.22436/jmcs.028.01.06 doi: 10.22436/jmcs.028.01.06 |
[14] | J. R. Graef, E. Tunc, S. R. Grace, Oscillatary and asymptotic behaviour of a third-order nonlinear neutral differential equation, Opusc. Math., 37 (2017), 839–852. |
[15] | G. Nithyakala, G. Ayyappan, J. Alzabut, E. Thandapani, Fourth-order nonlinear strongly non-canonical delay differential equations: New oscillation criteria via canonical transform, Math. Slovaca, 74 (2024), 115–126. http://dx.doi.org/10.1515/ms-2024-0008 doi: 10.1515/ms-2024-0008 |
[16] | A. Al-Jaser, B. Qaraad, O. Bazighifan, L. F. Iambor, Second-order neutral differential equations with distributed deviating arguments: Oscillatory behavior, AIMS Math., 11(2023), 2605. http://dx.doi.org/10.3390/math11122605 doi: 10.3390/math11122605 |
[17] | A. Almutairi, A. H. Ali, O. Bazighifan, L. F. Iambor, Oscillatory properties of Fourth-Order advanced differential equations, Mathematics, 11 (2023), 1–14. http://dx.doi.org/10.3390/math11061391 doi: 10.3390/math11061391 |
[18] | P. Gopalakrishnan, A. Murugesan, C. Jayakumar, Oscillation conditions of the second-order noncanonical difference equations, J. Math. Computer Sci., 25 (2022), 351–360. http://dx.doi.org/10.22436/jmcs.025.04.05 doi: 10.22436/jmcs.025.04.05 |
[19] | G. Purushothaman, K. Suresh, E. Tunc, E. Thandapani, Oscillation criteria of fourth-order nonlinear semi-canonical neutral differential equations via a canonical tranfsform, Elect. J. Differ. Equ., 2023 (2023), 1–12. http://dx.doi.org/10.58997/ejde.2023.70 doi: 10.58997/ejde.2023.70 |
[20] | J. Alzabut, S. R. Grace, G. N. Chhatria, New oscillation results for higher order nonlinear differential equations with a nonlinear neutral terms, J. Math. Computer Sci., 28 (2023), 294–305. http://dx.doi.org/10.22436/jmcs.028.03.07 doi: 10.22436/jmcs.028.03.07 |
[21] | S. K. Marappan, A. Almutairi, L. F. Iambor, O. Bazighifan, Oscillation of Emden-Fowler-Type differential equations with Non-Canonical operators and mixed neutral terms, Symmetry, 15 (2023), 553. http://dx.doi.org/10.3390/sym15020553 doi: 10.3390/sym15020553 |
[22] | J. Dzurina, E. Thandapani, S. Tamilvanan, Oscillation of soluations to third-order half-linear neutral differential equations, Electron. J. Differential Equations, 2012 (2012), 1–11. |
[23] | C. Trusdell, Rational mechanics, New York: Academic Press, 1983. |
[24] | G. E. Chatzarakis, S. R. Grace, I. Jadlovska, Oscillation criteria for third-order delay differential equations, Adv. Differ. Equ., 2017 (2017), 1–11. http://dx.doi.org/10.1186/s13662-017-1384-y doi: 10.1186/s13662-017-1384-y |
[25] | T. Candan, Asymptotic properties of solutions of third-order nonlinear neutral dynamic equations, Adv. Differ. Equ., 2014 (2014), 1–10. http://dx.doi.org/10.1186/1687-1847-2014-35 doi: 10.1186/1687-1847-2014-35 |
[26] | T. X. Li, C. H. Zhang, G. J. Xing, Oscillation of third-order neutral delay differential equations, Abstr. Appl. Anal., 2012 (2012), 1–11. http://dx.doi.org/10.1155/2012/569201 doi: 10.1155/2012/569201 |