Asymptotic properties of a class of delay differential equations with a sub-linear neutral term

HAN Zhongyue; YU Yuanhong

doi:10.3969/j.issn.1000-5641.201911020

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HAN Zhongyue, YU Yuanhong. Asymptotic properties of a class of delay differential equations with a sub-linear neutral term[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 1-7. doi: 10.3969/j.issn.1000-5641.201911020

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HAN Zhongyue, YU Yuanhong. Asymptotic properties of a class of delay differential equations with a sub-linear neutral term[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 1-7. doi: 10.3969/j.issn.1000-5641.201911020

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Asymptotic properties of a class of delay differential equations with a sub-linear neutral term

doi: 10.3969/j.issn.1000-5641.201911020

HAN Zhongyue^1
,,
YU Yuanhong²

1.
School of Mathematics and Big Data, Dezhou University, Dezhou Shandong　253023, China
2.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing　100190, China

Received Date: 2019-05-07
Publish Date: 2021-01-27

Abstract

Abstract

This paper studies the oscillation and asymptotic properties of delay differential equations with damping and sub-linear neutral terms using the generalized Riccati transformation technique and the mean value theorem. After analyzing the function of the cross-link between the condition $\int^\infty_{t_0}(\frac{1}{R(t)})^{\frac{1}{\gamma}}{\rm{d}}t=\infty$ and the relationship of parameters $\gamma$ and $\beta$ in the differential equations oscillation, the sufficient conditions for the existence of vibration solutions are provided to extend the existing results in the cited literature. Lastly, some applications are given to illustrate the significance of these results.
- damping,
- delay,
- sub-linear neutral terms,
- differential equations,
- oscillation

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References(14)

References

[1]	SUN Y G, MENG F W. Note on the paper of Džurina and Stavroulakis [J]. Applied Mathematics and Computation, 2006, 174(2): 1634-1641. doi: 10.1016/j.amc.2005.07.008
[2]	DŽURINA J, STAVROULAKIS I P. Oscillation criteria for second-order delay differential equations [J]. Applied Mathematics and Computation, 2003, 140(2): 445-453.
[3]	韩忠月. 具有强迫项的二阶中立型微分方程的振动准则 [J]. 生物数学学报, 2016, 31(1): 55-64.
[4]	WANG Q R, YANG Q G. Interval criteria for oscillation of second-order half-linear differential equations [J]. Journal of Mathematical Analysis and Applications, 2004, 291(1): 224-236. doi: 10.1016/j.jmaa.2003.10.028
[5]	LI W T. Interval oscillation of second-order half-linear functional differential equations [J]. Applied Mathematics and Computation, 2004, 155(2): 451-468. doi: 10.1016/S0096-3003(03)00790-2
[6]	杨甲山. 具非线性中立项的二阶变时滞微分方程的振荡性 [J]. 华东师范大学学报(自然科学版), 2016(4): 30-37.
[7]	张伟鹏, 毕平, 朱德明. Oscillation of certain second-order nonlinear differential equations with impulses [J]. 华东师范大学学报(自然科学版), 2007(3): 39-48.
[8]	曾云辉, 罗李平, 俞元洪. 中立性Emder-Fowler时滞微分方程的振动性 [J]. 数学物理学报, 2015, 35A(4): 803-814. doi: 10.3969/j.issn.1003-3998.2015.04.016
[9]	HAN Z Y, LIU Y D, SUN Q, et al. Oscillation criteria for new generalized Emden-Fowler equation [J]. 生物数学学报, 2017, 32(3): 273-282.
[10]	BOHNER M, SAKER S H. Oscillation of damped second order nonlinear delay differential equations of Emden-Fowler type [J]. Advances in Dynamical Systems and Applications, 2006, 1(2): 163-182.
[11]	TAMILVANAN S, THANDAPANI E, DŽURINA J. Oscillation of second order nonlinear differential equation with sub-linear neutral term [J]. Differential Equations and Applications, 2017, 9(1): 29-35.
[12]	TAMILVANAN S, THANDAPANI E, GRACE S R. Oscillation theorems of second order nonlinear differential equation with a non-linear neutral term [J]. International Journal of Dynamical Systems and Differential Equations, 2017, 7(4): 316-327. doi: 10.1504/IJDSDE.2017.087501
[13]	PHILOS C G. On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delay [J]. Archiv der Mathematik, 1981, 36(2): 168-178.
[14]	BACULÍKOVÁ B, DŽURINA J. Oscillation theorems for second order nonlinear neutral differential equations [J]. Computers and Mathematics with Applications, 2011, 62(12): 4472-4478. doi: 10.1016/j.camwa.2011.10.024