Результаты анализа колебаний для дифференциального уравнения второго порядка с запаздыванием и несколькими отклоняющимися аргументами

Исследуется колебательное поведение всех решений дифференциального уравнения второго порядка с запаздыванием, имеющего несколько отклоняющихся аргументов и неотрицательных коэффициентов. Получены некоторые достаточные условия для колебаний. Приведен также пример, иллюстрирующий значимость наших основных результатов.

1. Khasanov J., Muminov S., Iskandarov S. Mathematical modelling of industrial ammonia synthesis using nonlinear reaction-diffusion equations. Nanosystems: Phys. Chem. Math., 2025, 16(6), P. 749–754.

2. Kumar S., Gandhi K.S. Modeling of precipiation reactions with time delays. Chemical Engineering Science, 1995, 50(18), P. 2935–2948.

3. Kyrychko Y.N., Blyuss K.B. Delay differential equations in nanoscale systems: From theory to applications. Philosophical Traansactions of the Royal Society A, 2020, 378(2179), P. 20190275.

4. Sellitto A., et. al. Heat transport with memory: A delay differential approach. European Physical Journal B, 2015, 88, P. 210.

5. Zhang W.M., et al. Time-delayed feedback control of a nonlinear nonmachanical resonator. Physical Review B, 2013, 87(11), P. 115439.

6. Myshkis A.D. Linear homogeneous differential equations of first order with deviating arguments. Uspekhi Mat. Nauk, 1950, 5, P. 160–162.

7. Agarwal R.P., Grace S.R. Oscillation theorems for certain neutral differential equations. Comp. Math. Appl., 1999, 38, P. 10–11.

8. Arino O., Gyori I. Jawhari A. Oscillation criteria in delay equations. J.Differential Equations, 1984, 53, P. 115–123.

9. Koplatadze R.G., Chanturija T.A. Oscillating and monotone solutions of first order differential equations with deviating arguments (Russian). Differentsial’nye Uravneniya, 1982, 8, P. 1463–1465.

10. Laddas G., Lakshmikantham V., Papadakis J.S. Oscillations of higher-order retarded differential equations generated by retarded arguments. Delay and Functional Differential Equations and Their Applications, Academic press, New York, 1972, P. 219–231.

11. Li B. Oscillations of first order delay differential equations. Proc. Amer. Math. Soc., 1996, 124, P. 3729–3737.

12. Hunt B.R., Yorke, J.A. When all solutions of x′ = Xqi(t)x(t − Ti(t)) oscillate.J. Differential Equations, 1984, 53, P. 139–145.

13. Gyori I., Ladas G. Oscillation Theory of Delay Differential Equations With Applications. Clarendon Press, Oxford, 1991.

14. Akca H., Chatzarakis G.E., and Savroulakis I.P. An oscillation criteria for delay differential equations with several non-monotone arguments. Appl. Math. Lett., 2016, 59, P. 101–108.

15. Braverman E., Chatzarakis G.E., Stavroulakis I.P. Iterative oscillation test for differential equations with several non-monotone arguments. Advances in Difference equation, 2016, 87, P. 1–18.

16. Chatzarakis G.E., Ocalan O., Ozturk S. Oscillations for differential equations with several deviating arguments. Pacific Journal of Applied Mathematics, 2015, 7(2), P. 119–131.

17. Chatzarakis G.E., Peicks H. Differential equation with several non-monotone arguments: An oscillation result. Appl. Math. lett., 2017, 68, P. 20–26.

18. Braverman E., Karpuz B. On Oscillation of Differential and Difference Equations with non-monotone delays. Appl. Math. Comp., 2011, 218, P. 3880–3887.

19. Fukagai N., Kusano T. Oscillation theory of first order functional differential equations with deviating arguments. Ann. Mat. Pura Appl., 1984, 136, P. 95–117.

20. Stavroulakis I.P. A survey on the oscillation of differential equations with several deviating arguments. J. Inequalities and Applications, 2014, 2014, P. 399.

21. Ocalan O., Kilic N., Sahin S., Ozkan U.M. Oscillation of Nonlinear Delay Differential Equations with Non-monotone Arguments.Int. Jour. of Anal. and Appl. 2017, 14(2), P. 147–154.

22. Ocalan O., Kilic N., Kilic U., Ozkan U.M., Ozturk S. Oscillatory behaviour for nonlinear differential equations with several non-monotone arguments. Comp. Meth. for Diff. Equa., 2020, 8(01), P. 14–27.

23. Baculikova B. Oscillation for second order differential equation with delay.Elec. J. Diff. Equa., 2018, 96, P. 1–9.

24. Agarwal R.P., Bohner M., Li W.T. Nonoscillation and oscillation: Theory for Functional Differential Equations, Marcel Decker, New York, 2004.