An iterative method for the qualitative analysis of nonlinear neutral delay differential equations. (English) Zbl 07887978
Summary: In this paper, the authors studied sufficient conditions to understand the oscillatory behavior of solutions of nonlinear neutral delay (and advanced) differential equation (E) with deviating arguments. Employing Banach fixed point theorem, the authors established the existence of bounded positive solutions of (E). The authors solved various examples using MATLAB software to understand the applications of the main theorems. Moreover, the authors analyzed the effect of delay terms on the behavior of solutions of (E). This paper has improved the results obtained in Basu [2] and Chatzarakis [11].
MSC:
| 34K11 | Oscillation theory of functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 47H10 | Fixed-point theorems |
Keywords:
neutral delay differential equations; existence and uniqueness; oscillatory behavior; effect of delay terms; Matlab algorithmsSoftware:
MatlabReferences:
| [1] | A. H. Ali, A. S. Jaber, M. T. Yaseen, M. Rasheed, O. Bazighifan, T. A. Nofal: A comparison of finite difference and finite volume methods with numerical simulations: Burger equation model, Complexity, (2022). |
| [2] | R. Basu : An iterative scheme for the oscillation criteria of a nonlinear delay differential equation with several deviating arguments, Asian-Eur. J. Math, 15(04), 2250071 (2022). · Zbl 1487.34122 |
| [3] | R. Basu : Study of Qualitative Behavior of Solutions of a Class of Nonlinear Neutral Delay Differential Equations, PhD Thesis, University of Hyderabad (2015). |
| [4] | Bazighifan, O.; Cesarano, C., A Philos-type oscillation criteria for fourth-order neutral differential equation, Symmetry, 12, 3, 379, 2020 · doi:10.3390/sym12030379 |
| [5] | Bazighifan, O.; Dassios, I., Riccati technique and asymptotic behavior of fourth order advanced differential equations, Mathematics, 8, 4, 590, 2020 · doi:10.3390/math8040590 |
| [6] | Bazighifan, O.; Kumam, P., Oscillation theorems for advanced differential equations with p-Laplacian like operators, Mathematics, 8, 5, 821, 2020 · doi:10.3390/math8050821 |
| [7] | E. Braverman, B. Karpuz : On oscillation of differential and difference equations with non-monotone delays, Appl. Math. Comput., 218, (2011), 3880-3887. · Zbl 1256.39013 |
| [8] | E. Braverman, G. E. Chatzarakis, I. P. Stavroulakis : Iterative oscillation tests for differential equations with several non-monotone arguments, Adv. Diff. Eqn., (2016), 2016:87. · Zbl 1348.34121 |
| [9] | G. E. Chatzarakis : Differential equations with non-monotone arguments, J. Math. Comput. Sci., 6, (2016), 5, 953-964. |
| [10] | G. E. Chatzarakis : On oscillation of differential equations with non-monotone deviating arguments, Mediterr. J. Math., 14, (2017), 82, 17pp. · Zbl 1369.34088 |
| [11] | G. E. Chatzarakis : Oscillation test for linear deviating differential equations, Appl. Math. Lett., 98, (2019), 352-358. · Zbl 1426.34084 |
| [12] | Chatzarakis, GE; Jadlovská, I., Improved iterative oscillation tests for first order deviating differential equations, Opuscula Math., 38, 3, 327-356, 2018 · Zbl 1405.34056 · doi:10.7494/OpMath.2018.38.3.327 |
| [13] | Chatzarakis, GE; Jadlovská, I., Oscillation in deviating differential equations using an iterative method, Commu. Math., 27, 2, 143-169, 2019 · Zbl 1464.34088 · doi:10.2478/cm-2019-0012 |
| [14] | Croix, D.; Licandro, O., Life expectancy and endogenous growth, Econ. Lett., 65, 255-263, 1999 · Zbl 1037.91569 · doi:10.1016/S0165-1765(99)00139-1 |
| [15] | L. Duan : Periodic solutions for a neutral delay predator-prey model with non-monotonic functional response, Electron. J. Qual. Theory Differ. Equ., 48, (2012), 1-15. · Zbl 1340.34314 |
| [16] | L. H. Erbe, Q. Kong, B. G. Zhang : Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, 1995. |
| [17] | Gopalsamy, K.; Zhang, BG, On a neutral delay logistic equation, Dyn. Stab. Systems, 2, 183-195, 1988 · Zbl 0665.34066 |
| [18] | Hadeler, KP, Neutral delay equations from and for population dynamics, Electron. J. Qual. Theory Differ. Equ., 11, 1-18, 2008 · Zbl 1211.34097 |
| [19] | C. U. Jamilla, R. G. Mendoza, V. P. Mendoza: Parameter estimation in neutral delay differential equations using genetic algorithm with multi-parent crossover, (2021), 3113677. |
| [20] | Y. Kuang : Global stability of Gause-type predator-prey systems, J. Math. Biol., 28, (1990), 463-474. · Zbl 0742.92022 |
| [21] | Y. Kuang : On neutral delay logistic Gause-type predator-prey systems, Dyn. Stab. Systems, 6, (1991), 173-189. · Zbl 0728.92016 |
| [22] | Y. Kuang : On neutral delay two-species Lotka-Volterra competitive systems, J. Austral. Math. SOC., Ser. B, 32, (1991), 311-326. · Zbl 0729.92024 |
| [23] | Y. Kuang : Delay Differential Equations with Applications to Population Dynamics, 191, Academy Press (1993). · Zbl 0777.34002 |
| [24] | Kubiaczyk, I.; Saker, SH, Oscillation and stability in nonlinear delay differential equations of population dynamics, Math. Comput. Model., 35, 295-301, 2002 · Zbl 1069.34107 · doi:10.1016/S0895-7177(01)00166-2 |
| [25] | X. Lin, S. Zhou, Z. Zou, Y. Li : Chaos and its communication application of fractional-order neutral differential systems, 2010 International Workshop on Chaos-Fractal Theory and its Applications. |
| [26] | D. Zhou : On some problems on oscillations of some functional differential equations of first order, J. Shandong University, 25, (1990), 434-442. · Zbl 0726.34060 |
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