دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,548
تعداد مقالات18,877
تعداد مشاهده مقاله63,103,815
تعداد دریافت فایل اصل مقاله22,970,063
Erdur, Sultan, Tunc, Cemil. (1402). On the existence of periodic solutions of third order delay differential equations. سامانه مدیریت نشریات علمی, 11(2), 319-331. doi: 10.22034/cmde.2022.50862.2112
Sultan Erdur; Cemil Tunc. "On the existence of periodic solutions of third order delay differential equations". سامانه مدیریت نشریات علمی, 11, 2, 1402, 319-331. doi: 10.22034/cmde.2022.50862.2112
Erdur, Sultan, Tunc, Cemil. (1402). 'On the existence of periodic solutions of third order delay differential equations', سامانه مدیریت نشریات علمی, 11(2), pp. 319-331. doi: 10.22034/cmde.2022.50862.2112
Erdur, Sultan, Tunc, Cemil. On the existence of periodic solutions of third order delay differential equations. سامانه مدیریت نشریات علمی, 1402; 11(2): 319-331. doi: 10.22034/cmde.2022.50862.2112

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)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50862.2112
نویسندگان
Sultan Erdur1؛ Cemil Tunc* 2
1Department of Mathematics Faculty of Arts and Sciences Gaziantep University 27310, Gaziantep, Turkey.
2Department 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.
آمار
تعداد مشاهده مقاله: 600
تعداد دریافت فایل اصل مقاله: 718


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب