时标上具非正中立项的二阶动力方程的动力学性质

Abstract

Abstract:

This paper is concerned with dynamical behavior of second-order nonlinear non-autonomous delay dynamic equations with a nonpositive neutral coefficient on a time scale T. By using the time scales theory and combining with the classical inequality, we establish some new dynamical properties for the equations. The dynamical properties of dynamic equations are further generalized and perfected.

Key words: Dynamical properties, Time scales, Dynamic equations, Riccati substitutions, Nonlinear

CLC Number:

O175.1

Ping Zhang,Jiashan Yang. Dynamical Properties of Second-Order Dynamic Equations with a Nonpositive Neutral Coefficient on a Time Scale[J].Acta mathematica scientia,Series A, 2021, 41(1): 217-226.

Trendmd

References 15

1	Bohner M , Peterson A . Dynamic Equations on Time Scales:An Introduction with Applications. Boston: Birkhauser, 2001
2	孙玉虹, 李德生, 李玉双. 具有阻尼项的二阶非线性时滞中立型动力方程的振动性. 浙江大学学报(理学版), 2018, 45 (2): 131- 135
	Sun Y H , Li D S , Li Y S . Oscillation of second-order nonlinear delay neutral dynamic equations with damping term. Journal of Zhejiang University (Science Edition), 2018, 45 (2): 131- 135
3	杨甲山, 李同兴. 时间模上一类二阶阻尼Emden-Fowler型动态方程的振荡性. 数学物理学报, 2018, 38A (1): 134- 155 doi: 10.3969/j.issn.1003-3998.2018.01.013
	Yang J S , Li T X . Oscillation for a class of second-order damped Emden-Fowler dynamic equations on time scales. Acta Mathematica Scientia, 2018, 38A (1): 134- 155 doi: 10.3969/j.issn.1003-3998.2018.01.013
4	杨甲山. 时间尺度上二阶Emden-Fowler型延迟动态方程的振动性. 振动与冲击, 2018, 37 (16): 154- 161
	Yang J S . Oscillation for a class of second-order Emden-Fowler-type delay dynamic equations on time scales. Journal of Vibration and Shock, 2018, 37 (16): 154- 161
5	杨甲山. 时间模上一类二阶非线性延迟动力系统的振动性分析. 应用数学学报, 2018, 41 (3): 388- 402
	Yang J S . Oscillation analysis of second-order nonlinear delay dynamic equations on time scales. Acta Mathematicae Applicatae Sinica, 2018, 41 (3): 388- 402
6	韩忠月. 二阶非线性中立型动力方程的振动定理. 华中师范大学学报(自然科学版), 2014, 48 (5): 627- 631
	Han Z Y . Oscillation theorems for second-order nonlinear neutral dynamic equations. Journal of Central China Normal University (Natural Sciences), 2014, 48 (5): 627- 631
7	杨甲山, 覃桂茳, 覃学文, 等. 一类二阶Emden-Fowler型微分方程的若干振动条件. 浙江大学学报(理学版), 2019, 46 (3): 302- 308
	Yang J S , Qin G J , Qin X W , et al. New oscillatory conditions of a class of the second-order Emden-Fowler differential equations. Journal of Zhejiang University (Science Edition), 2019, 46 (3): 302- 308
8	Bohner M , Li T X . Oscillation of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient. Applied Mathematics Letters, 2014, 37: 72- 76 doi: 10.1016/j.aml.2014.05.012
9	Zhang M , Chen W , El-Sheikh Mma , et al. Oscillation criteria for second-order nonlinear delay dynamic equations of neutral type. Advances in Difference Equations, 2018, 2018: 26 doi: 10.1186/s13662-018-1474-5
10	Deng X H , Wang Q R , Zhou Z . Oscillation criteria for second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients on time scales. Sci China Math, 2017, 60: 113- 132 doi: 10.1007/s11425-016-0070-y
11	邱仰聪, 王其如. 具可变号系数的二阶时标动态方程的振动准则. 应用数学学报, 2016, 39 (1): 121- 129
	Qiu Y C , Wang Q R . Oscillation criteria for second-order dynamic equations with oscillatory coefficients on time scales. Acta Mathematicae Applicatae Sinica, 2016, 39 (1): 121- 129
12	覃桂茳, 杨甲山. 时标上一类二阶非线性动态方程振动性的新准则. 安徽大学学报(自然科学版), 2019, 43 (1): 24- 31
	Qin G J , Yang J S . New criteria for oscillation of certain second-order nonlinear dynamic equations on time scales. Journal of Anhui University (Natural Science Edition), 2019, 43 (1): 24- 31
13	罗李平, 俞元洪, 曾云辉. 三阶非线性时滞微分方程振动性的新准则. 应用数学和力学, 2013, 34 (9): 941- 947
	Luo L P , Yu Y H , Zeng Y H . New criteria for oscillation of third order nonlinear delay differential equations. Applied Mathematics and Mechanics, 2013, 34 (9): 941- 947
14	曾云辉, 罗李平, 俞元洪. 中立型Emden-Fowler时滞微分方程的振动性. 数学物理学报, 2015, 35A (4): 803- 814 doi: 10.3969/j.issn.1003-3998.2015.04.016
	Zeng Y H , Luo L P , Yu Y H . Oscillation for Emden-Fowler delay differential equations of neutral type. Acta Mathematica Scientia, 2015, 35A (4): 803- 814 doi: 10.3969/j.issn.1003-3998.2015.04.016
15	覃桂茳, 杨甲山, 刘玉周. 一类具非线性中立项的二阶微分方程的振动性. 安徽大学学报(自然科学版), 2020, 44 (1): 31- 36
	Qin G J , Yang J S , Liu Y Z . Oscillation of certain second-order differential equations with nonlinear neutral term. Journal of Anhui University (Natural Science Edition), 2020, 44 (1): 31- 36

[1]	Qin Li,Zuodong Yang. Multiple Positive Solutions for a Quasilinear Elliptic System Involving the Caffarelli-Kohn-Nirenberg Inequality and Nonlinear Boundary Conditions [J]. Acta mathematica scientia,Series A, 2020, 40(6): 1634-1645.
[2]	Wencui Liang,Zhengjie Zhang. Multiple Solutions for Nonlinear Equations Related to Kirchhoff Type Equations [J]. Acta mathematica scientia,Series A, 2020, 40(4): 842-849.
[3]	Ping Shi. Existence and Uniqueness of Fixed Points for a Class of Abstract Binary Nonlinear Operators [J]. Acta mathematica scientia,Series A, 2020, 40(4): 882-890.
[4]	Zhiyu Zhang,Feifei Song,Tongxing Li,Yuanhong Yu. Oscillation Criteria of Second Order Nonlinear Neutral Emden-Fowler Differential Equations with Damping [J]. Acta mathematica scientia,Series A, 2020, 40(4): 934-946.
[5]	Jian Liu,Zhixin Zhang,Wei Jiang. Global Mittag-Leffler Stability of Fractional Order Nonlinear Impulsive Differential Systems with Time Delay [J]. Acta mathematica scientia,Series A, 2020, 40(4): 1053-1060.
[6]	Guodong Ma. A Strongly Convergent Generalized Gradient Projection Method for Minimax Optimization with General Constraints [J]. Acta mathematica scientia,Series A, 2020, 40(3): 641-649.
[7]	Liping Luo,Zhenguo Luo,Yunhui Zeng. Oscillation Conditions of Certain Nonlinear Impulsive Neutral Parabolic Distributed Parameter Systems [J]. Acta mathematica scientia,Series A, 2020, 40(3): 784-795.
[8]	Keang Fu,Li Ding,Junqiao Li. Asymptotics for the Self-Weighted M-Estimation of Nonlinear Autoregressive Models with Heavy-Tailed Errors [J]. Acta mathematica scientia,Series A, 2020, 40(2): 475-483.
[9]	Yijia Ma,Liugen Xue,Fei Lu. Statistical Inference in Partially Nonlinear Varying-Coefficient Errors-in-Variables Models with Missing Responses [J]. Acta mathematica scientia,Series A, 2020, 40(2): 460-474.
[10]	Shimin Xu,Chunhua Wang. Local Uniqueness of a Single Peak Solution of a Subcritical Kirchhoff Problem in R³ [J]. Acta mathematica scientia,Series A, 2020, 40(2): 432-440.
[11]	Jimeng Li,Jiashan Yang. Philos-Type Criteria for Second-Order Delay Differential Equations with Nonlinear Neutral Term [J]. Acta mathematica scientia,Series A, 2020, 40(1): 169-186.
[12]	Na Wei. The Solvability of Dual Minkowski Problem in $\mathbb{R}$² [J]. Acta mathematica scientia,Series A, 2019, 39(6): 1314-1322.
[13]	Yan Luo,Wenzhe Xie. Existence of Solutions for Impulsive Differential Inclusions with Upper and Lower Solutions in the Reverse Order [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1055-1063.
[14]	Yanfang Mei,Youjun Wang. Three Types of Solutions for a Class of Nonlinear Schrödinger Equations [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1087-1093.
[15]	Zhiyu Zhang,Yuanhong Yu,Shuping Li,Shizhu Qiao. Oscillation of Second Order Nonlinear Differential Equations with Neutral Delay [J]. Acta mathematica scientia,Series A, 2019, 39(4): 797-811.

Dynamical Properties of Second-Order Dynamic Equations with a Nonpositive Neutral Coefficient on a Time Scale

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 15

Related Articles 15

Metrics

Comments

Recommended 10