时标上具非正中立项的二阶动力方程的动力学性质

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 217-226.

时标上具非正中立项的二阶动力方程的动力学性质

张萍¹(),杨甲山^2,*()

¹ 邵阳学院理学院湖南邵阳 422004
² 梧州学院大数据与软件工程学院广西梧州 543002

收稿日期:2019-12-06 出版日期:2021-02-26 发布日期:2021-01-29
通讯作者: 杨甲山 E-mail:411451097@qq.com;syxyyjs@163.com
作者简介:张萍, E-mail: 411451097@qq.com
基金资助:
国家自然科学基金项目(51765060);湖南省教育厅一般项目(20C1683)

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

Ping Zhang¹(),Jiashan Yang^2,*()

¹ School of Science, Shaoyang University, Hunan Shaoyang 422004
² School of Data Science and Software Engineering, Wuzhou University, Guangxi Wuzhou 543002

Received:2019-12-06 Online:2021-02-26 Published:2021-01-29
Contact: Jiashan Yang E-mail:411451097@qq.com;syxyyjs@163.com
Supported by:
the NSFC(51765060);the Science Project of Hunan Provence EducationDepartment(20C1683)

摘要/Abstract

摘要：

研究时标T上的一类具非正中立项的非线性非自治二阶动力方程的动力学性质.利用时标上的有关理论，并结合一些经典不等式，得到了该方程的一些新的动力学性质，进一步推广和完善了动力方程的动力学性质.

关键词: 动力学性质, 时标, 动力方程, Riccati变换, 非线性

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

中图分类号:

O175.1

张萍,杨甲山. 时标上具非正中立项的二阶动力方程的动力学性质[J]. 数学物理学报, 2021, 41(1): 217-226.

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.

参考文献 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]	李琴,杨作东. 含Caffarelli-Kohn-Nirenberg不等式和非线性边界条件的拟线性椭圆型方程组的多解性[J]. 数学物理学报, 2020, 40(6): 1634-1645.
[2]	梁文翠,张正杰. Kirchhoff型方程有关的非线性方程多解的存在性[J]. 数学物理学报, 2020, 40(4): 842-849.
[3]	史平. 一类抽象二元非线性算子的不动点的存在性与唯一性[J]. 数学物理学报, 2020, 40(4): 882-890.
[4]	仉志余,宋菲菲,李同兴,俞元洪. 带阻尼项的二阶非线性中立型Emden-Fowler微分方程的振动准则[J]. 数学物理学报, 2020, 40(4): 934-946.
[5]	刘健,张志信,蒋威. 分数阶非线性时滞脉冲微分系统的全局Mittag-Leffler稳定性[J]. 数学物理学报, 2020, 40(4): 1053-1060.
[6]	方芳,胡贝贝,张玲. 超广义Burgers方程族的非线性可积耦合及其Bargmann对称约束[J]. 数学物理学报, 2020, 40(3): 694-704.
[7]	罗李平,罗振国,曾云辉. 一类非线性脉冲中立抛物型分布参数系统的振动条件[J]. 数学物理学报, 2020, 40(3): 784-795.
[8]	马国栋. 一般约束极大极小优化问题一个强收敛的广义梯度投影算法[J]. 数学物理学报, 2020, 40(3): 641-649.
[9]	许诗敏,王春花. Kirchhoff方程单峰解的局部唯一性[J]. 数学物理学报, 2020, 40(2): 432-440.
[10]	马奕佳,薛留根,芦飞. 缺失数据下部分非线性变系数EV模型的统计推断[J]. 数学物理学报, 2020, 40(2): 460-474.
[11]	傅可昂,丁丽,李君巧. 重尾非线性自回归模型自加权M-估计的渐近分布[J]. 数学物理学报, 2020, 40(2): 475-483.
[12]	李继猛,杨甲山. 具非线性中立项的二阶延迟微分方程的Philos型准则[J]. 数学物理学报, 2020, 40(1): 169-186.
[13]	魏娜. $\mathbb{R}$²上对偶Minkowski问题的可解性[J]. 数学物理学报, 2019, 39(6): 1314-1322.
[14]	梅艳芳,王友军. 一类非线性Schrödinger方程三种类型的解[J]. 数学物理学报, 2019, 39(5): 1087-1093.
[15]	李继猛. 二阶广义Emden-Fowler型延迟微分方程的振荡性分析[J]. 数学物理学报, 2019, 39(5): 1041-1054.