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Taie, R. O. A.; Bakhit, D. A. M.

Existence and uniqueness criterion of a periodic solution for a third-order neutral differential equation with multiple delay. (English) Zbl 1514.34120

Bound. Value Probl. 2023, Paper No. 25, 21 p. (2023).
Summary: In this paper, we study the existence and uniqueness of a periodic solution for a third-order neutral delay differential equation (NDDE) by applying Mawhin’s continuation theorem of coincidence degree and analysis techniques. An illustrative example is given as an application to support our results. To confirm the accuracy of our results, we also present a plot of the behavior of the periodic solution.

Cited in 1 Document

MSC:

34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations

Keywords:

existence and uniqueness; neutral delay differential equation; Mawhin’s continuation theorem
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[1] Abou-El-Ela, A. M.A.; Sadek, A. I.; Mahmoud, A. M., Periodic solutions for a kind of third-order delay differential equations with a deviating argument, J. Math. Sci. Univ. Tokyo, 18, 35-49 (2011) · Zbl 1259.34058
[2] Abou-El-Ela, A. M.A.; Sadek, A. I.; Mahmoud, A. M., Existence and uniqueness of a periodic solution for third-order delay differential equation with two deviating arguments, Int. J. Appl. Math., 42, 1, 7-12 (2012) · Zbl 1512.34122
[3] Ademola, A. T.; Ogundare, B. S.; Adesina, O. A., Stability, boundedness, and existence of periodic solutions to certain third-order delay differential equations with multiple deviating arguments, Int. J. Differ. Equ., 2015 (2015) · Zbl 1339.34072
[4] Bainov, D. D.; Mishev, D. P., Oscillation Theory for Neutral Differential Equations with Delay (1991), Bristol: IOP Publishing, Bristol · Zbl 0747.34037
[5] Biçer, E., On the periodic solutions of third-order neutral differential equation, Math. Methods Appl. Sci., 44, 2013-2020 (2021) · Zbl 1476.34147 · doi:10.1002/mma.6906
[6] Burton, T. A., Stabitity and Periodic Solutions of Ordinary and Functional Differential Equations (1985), San Diego: Academic Press, San Diego · Zbl 0635.34001
[7] Fikadu, T. T.; Wedajo, A. G.; Gurmu, E. D., Existence and uniqueness of solution of a neutral functional differential equation, Int. J. Math. Comput. Res., 9, 4, 2271-2276 (2021)
[8] Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Berlin: Springer, Berlin · Zbl 0339.47031 · doi:10.1007/BFb0089537
[9] Graef, J. R.; Beldjerd, D.; Remili, M., On the stability, boundedness, and square integrability of solutions of third-order neutral delay differential equations, Math. J. Okayama Univ., 63, 1-14 (2021) · Zbl 1459.34169
[10] Gui, Z., Existence of positive periodic solutions to third-order delay differential equations, Electron. J. Differ. Equ., 2006 (2006) · Zbl 1118.34055
[11] Hale, J., Theory of Functional Differential Equations (1977), New York: Springer, New York · Zbl 0352.34001 · doi:10.1007/978-1-4612-9892-2
[12] Iyase, S. A.; Adeleke, O. J., On the existence and uniqueness of periodic solution for a third-order neutral functional differential equation, Int. J. Math. Anal., 10, 17, 817-831 (2016) · doi:10.12988/ijma.2016.6345
[13] Kolmannovskii, V.; Myshkis, A., Introduction to the Theory and Applications of Functional Differential Equations (1999), Berlin: Springer, Berlin · Zbl 0917.34001 · doi:10.1007/978-94-017-1965-0
[14] Kong, F.; Lu, S.; Liang, Z., Existence of positive periodic neutral Lienard differential equations with a singularity, Electron. J. Differ. Equ., 2015 (2015) · Zbl 1336.34099
[15] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics (1993), New York: Academic Press, New York · Zbl 0777.34002
[16] Liu, B.; Huang, L., Periodic solutions for a kind of Rayleigh equation with a deviating argument, J. Math. Anal. Appl., 321, 491-500 (2006) · Zbl 1103.34062 · doi:10.1016/j.jmaa.2005.08.070
[17] Lu, B.; Ge, W., Periodic solutions for a kind of second-order differential equation with multiple deviating arguments, Appl. Math. Comput., 146, 1, 195-209 (2003) · Zbl 1037.34065
[18] Mahmoud, A. M., Existence and uniqueness of periodic solutions for a kind of third-order functional differential equation with a time-delay, Differ. Equ. Control Process., 2, 192-208 (2018) · Zbl 1411.34098
[19] Mahmoud, A. M.; Farghaly, E. S., Existence of periodic solution for a kind of third-order generalized neutral functional differential equation with variable parameter, Ann. App. Math., 34, 3, 285-301 (2018) · Zbl 1424.34237
[20] Mahmoud, A. M.; Farghaly, E. S., Periodic solutions for a kind of fourth-order neutral functional differential equation, Arctic J., 72, 6, 68-85 (2019)
[21] Oudjedi, L. D.; Lekhmissi, B.; Remili, M., Asymptotic properties of solutions to third-order neutral differential equations with delay, Proyecciones, 38, 1, 111-127 (2019) · Zbl 1447.34065 · doi:10.4067/S0716-09172019000100111
[22] Taie, R. O.A.; Alwaleedy, M. G.A., Existence and uniqueness of a periodic solution to a certain third-order neutral functional differential equation, Math. Commun., 27, 2022, 257-276 (2022) · Zbl 1516.34103
[23] Wei, M.; Jiang, C.; Li, T., Oscillation of third-order neutral differential equations with damping and distributed delay, Adv. Differ. Equ., 2019 (2019) · Zbl 1487.34130 · doi:10.1186/s13662-019-2363-2
[24] Xin, Y.; Cheng, Z., Neutral operator with variable parameter and third-order neutral differential equation, Adv. Differ. Equ., 273, 1687-1847 (2014) · Zbl 1417.34168
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