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## On the existence of periodic solutions of third order delay differential equations | ||

Computational Methods for Differential Equations | ||

مقاله 9، دوره 11، شماره 2، تیر 2023، صفحه 319-331
اصل مقاله (304.94 K)
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نوع مقاله: Research Paper | ||

شناسه دیجیتال (DOI): 10.22034/cmde.2022.50862.2112 | ||

نویسندگان | ||

Sultan Erdur^{1}؛ Cemil Tunc ^{} ^{} ^{2}
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^{1}Department of Mathematics Faculty of Arts and Sciences Gaziantep University 27310, Gaziantep, Turkey. | ||

^{2}Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, VAN, Turkey. | ||

چکیده | ||

This work deals with the existence of periodic solutions (EPSs) to a third order nonlinear delay differential equation (DDE) with multiple constant delays. For the considered DDE, a theorem is proved, which includes sufficient criteria related to the EPSs. The technique of the proof depends on Lyapunov-Krasovskiˇı functional (LKF) approach. The obtained result extends and improves some results that can be found in the literature. In a particular case of the considered DDE, an example is provided to show the applicability of the main result of this paper. | ||

کلیدواژهها | ||

Existence؛ Periodic solutions؛ Differential equation؛ Third order؛ Delay؛ LKF | ||

مراجع | ||

- [1] A. M. A. Abou-El-Ela, A. I. Sadek, and A. M. Mahmoud, Existence and uniqueness of a periodic solution for third-order delay differential equation with two deviating arguments, IAENG Int. J. Appl. Math., 42(1) (2012), 7–12.
- [2] A. M. A. Abou-El-Ela, A. I. Sadek, and R. O. A. Taie, Existence of periodic solutions to third-order nonlinear delay differential equation, Ann. Differential Equations, 27(4) (2011), 409–417.
- [3] A. T. Ademola, Existence and uniqueness of a periodic solution to certain third order nonlinear delay differential equation with multiple deviating arguments, Acta Univ. Sapientiae Math., 5(2) (2013), 113–131.
- [4] A. T. Ademola, M. O. Ogundiran, and P. O. Arawomo, Stability, boundedness and existence of periodic solutions to certain third order nonlinear differential equations. Acta Univ. Palack. Olomuc, Fac. Rerum Natur. Math., 54(1) (2015), 5–18.
- [5] A. T. Ademola, B. S. Ogundare, M. O. Ogundiran, and O. A. Adesina, Stability, boundedness, and existence of periodic solutions to certain third-order delay differential equations with multiple deviating arguments, Int. J. Differ. Equ., (2015), 12 pp.
- [6] A. U. Afuwape and J. E. Castellanos, On the existence of periodic solution of a nonlinear third-order differential equation using the nonlocal reduction method, J. Nigerian Math. Soc., 26 (2007), 75–80.
- [7] J. Alzabut and C. Tun¸c, Existence of periodic solutions for Rayleigh equations with state-dependent delay, Electron. J. Differential Equations, 77 (2012), 8 pp.
- [8] Y. J. Chen and H. Yang, Existence of periodic solutions of a class of third-order delay differential equations in Banach spaces, (Chinese) J. Shandong Univ. Nat. Sci., 53(8) (2018), 84–94.
- [9] E. N. Chukwu, On the boundedness and the existence of a periodic solution of some nonlinear third order delay differential equation, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat., 64(5) (1978), 440–447.
- [10] R. Doroudi, Existence of periodic solution for a class of linear third order ODE, J. Math. Ext., 4(1) (2009), 61–72.
- [11] J. O. C. Ezeilo, Further results on the existence of periodic solutions of a certain third order differential equation, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat., 63(6) (1977), 493–503.
- [12] J. O. C. Ezeilo, Further results on the existence of periodic solutions of a certain third-order differential equation, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat., 64(1) (1978), 48–58.
- [13] C. Feng, On the existence of periodic solutions for a certain system of third order nonlinear differential equations, Ann. Differential Equations, 11(3) (1995), 264–269.
- [14] J. R. Graef, D. Beldjerd, and M. Remili, On stability, ultimate boundedness, and existence of periodic solutions of certain third order differential equations with delay, PanAmer. Math. J., 25(1) (2015), 82–94.
- [15] J. R. Graef and C. Tun¸c, Global asymptotic stability and boundedness of certain multi-delay functional differential equations of third order, Math. Methods Appl. Sci., 38(17) (2015), 3747–3752.
- [16] J. Z. Huang, P. C. Li, and C. H. Fu, Existence of almost periodic solutions for a class of third-order differential equations with delay, (Chinese) Pure Appl. Math., 29(5) (2013), 465–471.
- [17] S. A. Iyase, On the existence of periodic solutions of certain third order non-linear differential equations with delay, Special issue in honour of Professor Chike Obi. J. Nigerian Math. Soc., 11(1) (1992), 27–35.
- [18] Y. Knezhevich-Milyanovich, Conditions for the existence of periodic solutions of third-order nonlinear differential equations, (Russian) Mat. Vesnik, 52(3-4) (2000), 79–82.
- [19] B. W. Liu, L. Huang, and L. Y. Hong, Existence of periodic solutions of a third-order functional differential equation, (Chinese) Acta Math. Appl. Sin., 29(2) (2006), 226–233.
- [20] A. M. Mahmoud, Existence and uniqueness of periodic solutions for a kind of third-order functional differential equation with a time-delay, Differ. Uravn. Protsessy Upr., (2) (2018), 192–208.
- [21] B. Mehri and M. Niksirat, On the existence of periodic solutions for the quasi-linear third-order differential equation, J. Math. Anal. Appl., 261(1) (2001), 159–167.
- [22] B. Mehri and M. Khalessizadeh, On the existence of periodic solutions for a certain non-linear third order differ- ential equation, Z. Angew. Math. Mech., 57(5) (1977), 241–243.
- [23] F. Minh´os, Periodic third order problems: existence and location result, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16 (2009), 182–186.
- [24] M. Remili and D. Beldjerd, On ultimate boundedness and existence of periodic solutions of kind of third order delay differential equations, Acta Univ. M. Belii Ser. Math., 24 (2016), 43–57.
- [25] Q. R. Shen, Existence and uniqueness of periodic solution for a third-order differential equation with delays, (Chinese) Xiamen Daxue Xuebao Ziran Kexue Ban, 53(3) (2014), 299–304.
- [26] H. O.,Tejumola, A note on the boundedness and the stability of solutions of certain third-order differential equa- tions, Ann. Mat. Pura Appl., 92(4) (1972), 65–75.
- [27] H. O. Tejumola and B. Tchegnani, Stability, boundedness and existence of periodic solutions of some third and fourth order nonlinear delay differential equations, J. Nigerian Math. Soc., 19 (2000), 9–19.
- [28] C. Tun¸c, On the existence of periodic solutions to nonlinear third order ordinary differential equations with delay, J. Comput. Anal. Appl., 12(1-B) (2010), 191–201.
- [29] C. Tun¸c, Existence of periodic solutions to nonlinear differential equations of third order with multiple deviating arguments, Int. J. Differ. Equ., (2012), 13 pp.
- [30] C. Tun¸c, Stability and boundedness of the nonlinear differential equations of third order with multiple deviating arguments, Afr. Mat., 24(3) (2013), 381–390.
- [31] C. Tun¸c, New results on the existence of periodic solutions for Rayleigh equation with state-dependent delay, J. Math. Fundam. Sci., 45(2) (2013), 154–162.
- [32] C. Tun¸c, Global stability and boundedness of solutions to differential equations of third order with multiple delays, Dynam. Systems Appl., 24(4) (2015), 467–478.
- [33] C. Tun¸c, On the existence of periodic solutions of functional differential equations of the third order, Appl. Comput. Math., 15(2) (2016), 189–199.
- [34] C. Tun¸c, Stability and boundedness in differential systems of third order with variable delay, Proyecciones, 35(3) (2016), 317–338.
- [35] C. Tun¸c, On the qualitative behaviors of nonlinear functional differential systems of third order, Advances in nonlinear analysis via the concept of measure of noncompactness, (2017), 421–439.
- [36] C. Tun¸c, A note on the stability and boundedness results of solutions of certain fourth order differential equations, Appl. Math. Comput., 155(3) (2004), 837–843.
- [37] C. Tun¸c and S. Erdur, On the existence of periodic solutions to certain non-linear differential equations of third order. Proc. Pak. Acad. Sci. A, 54(2) (2017), 207–218.
- [38] C. Tun¸c and O. Tun¸c, On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order, Journal of Advanced Research, 7(1), (2016), 165-168.
- [39] O. Tun¸c, On the behaviors of solutions of systems of non-linear differential equations with multiple constant delays, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 115(4) (2021), 22 pp.
- [40] V. Vlˇcek, Note on existence of periodic solutions to the third-order nonlinear differential equation, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 29 (1990), 165–195.
- [41] T. Yoshizawa, Stability theory by Liapunov’s second method, Publications of the Mathematical Society of Japan, 9 The Mathematical Society of Japan, Tokyo 1966.
- [42] Z. Yu, A. S. G. Abdel-Salam, A. Sohail, and F. Alam, Forecasting the impact of environmental stresses on the frequent waves of COVID19, Nonlinear Dynamics, 106(2), (2021), 1509-1523.
- [43] Z. Yu, R. Arif, M. A. Fahmy, and A. Sohail, Self organizing maps for the parametric analysis of COVID-19 SEIRS delayed model, Chaos, Solitons & Fractals, 150 (2021), 111202.
- [44] Z. Yu, R. Ellahi, A. Nutini, A. Sohail, and M. S. Sait, Modeling and simulations of CoViD-19 molecular mechanism induced by cytokines storm during SARS-CoV2 infection, Journal of Molecular Liquids, 327 (2021), 114863.
- [45] Z. Yu, A. Sohail, A. Nutini, and R. Arif, Delayed modeling approach to forecast the periodic behavior of SARS-2, Frontiers in Molecular Biosciences, (2021), 386.
- [46] Z. Yu, A. Sohail, T. A. N. Nofal, and J. M. R. S. Tavares, Explainability of neural network clustering in interpreting the COVID-19 emergency data, Fractals, 30(5) (2022), 12pp.
- [47] Y. F. Zhu, On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system, Ann. Differential Equations, 8(2) (1992), 249–259.
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