脉冲扰动对非线性时滞双曲型分布参数系统振动的影响

数学物理学报 ›› 2018, Vol. 38 ›› Issue (2): 313-321.

脉冲扰动对非线性时滞双曲型分布参数系统振动的影响

罗李平, 罗振国, 邓义华

衡阳师范学院数学与统计学院湖南衡阳 421002

收稿日期:2017-05-25 修回日期:2017-08-29 出版日期:2018-04-26 发布日期:2018-04-26
通讯作者: 罗振国 E-mail:luolp3456034@163.com
基金资助:
湖南省自然科学基金面上项目（2016JJ2008）、湖南省教育厅重点项目（17A030）、湖南省青年骨干教师培养对象（[2015]361）、湖南省重点实验室项目（2016TP1020）和湖南省重点建设学科项目

Effect of Impulsive Perturbations on Oscillation of Nonlinear Delay Hyperbolic Distributed Parameter Systems

Luo Liping, Luo Zhenguo, Deng Yihua

College of Mathematics and Statistics, Hengyang Normal University, Hunan Hengyang 421002

Received:2017-05-25 Revised:2017-08-29 Online:2018-04-26 Published:2018-04-26
Supported by:
Supported by the Hunan Provincial Natural Science Foundation (2016JJ2008), the Key Project of Hunan Provincial Education Department (17A030), the Training Target of the Young Backbone Teachers in Hunan Colleges and Universities ([2015]361), the Project of Hunan Provincial Key Laboratory (2016TP1020) and the Construct Program of the Key Discipline in Hunan Province

摘要/Abstract

摘要： 研究一类具高阶Laplace算子的非线性脉冲时滞双曲型分布参数系统在第三类边值条件下的振动性质，借助处理高阶Laplace算子的技巧和脉冲时滞微分不等式，建立了这类系统振动的若干新的显式充分判据.所得结论充分显示这种振动性是由于脉冲扰动和时滞效应所引起的.

关键词: 振动性, 双曲型分布参数系统, 高阶Laplace算子, 非线性, 脉冲扰动, 时滞效应

Abstract: The oscillatory behavior for a class of nonlinear impulsive delay hyperbolic distributed parameter systems with higher order Laplace operator are investigated under third boundary value condition. By employing the technique of treating higher order Laplace operator and impulsive delay differential inequality, some new explicit sufficient criteria are established for the oscillation of such systems. The conclusions obtained fully show that the oscillation is caused by impulsive perturbation and delay effect.

Key words: Oscillation, Hyperbolic distributed parameter system, Higher order Laplace operator, Nonlinear, Impulsive perturbation, Delay effect

中图分类号:

O175.27

罗李平, 罗振国, 邓义华. 脉冲扰动对非线性时滞双曲型分布参数系统振动的影响[J]. 数学物理学报, 2018, 38(2): 313-321.

Luo Liping, Luo Zhenguo, Deng Yihua. Effect of Impulsive Perturbations on Oscillation of Nonlinear Delay Hyperbolic Distributed Parameter Systems[J]. Acta mathematica scientia,Series A, 2018, 38(2): 313-321.

参考文献

[1] 罗李平, 罗振国, 杨柳. 具脉冲扰动和时滞效应的拟线性抛物系统的(强)振动分析. 应用数学学报, 2016, 39(1):21-30Luo Liping, Luo Zhenguo, Yang Liu. (Strong) Oscillation analysis of quasilinear parabolic systems with impulse perturbation and delay effect. Acta Mathematicae Applicatae Sinica, 2016, 39(1):21-30
[2] 马晴霞, 刘安平. 脉冲时滞中立双曲型方程组的振动性. 数学物理学报, 2016, 36A(3):462-472Ma Qingxia, Liu Anping. Oscillation of neutral impulsive hyperbolic systems with deviating arguments. Acta Mathematica Scientia, 2016, 36A(3):462-472
[3] Ning X Q, You S J. Oscillation of the systems of impulsive hyperbolic partial differential equations. Journal of Chemical and Pharmaceutical Research, 2014, 6(7):1370-1377
[4] Ma Q X, Liu A P. Oscillation criteria of neutral type impulsive hyperbolic equations. Acta Mathematica Scientia, 2014, 34B(6):1845-1853
[5] 罗李平, 曾云辉, 罗振国. 具脉冲和时滞效应的拟线性双曲系统的振动性定理. 应用数学学报, 2014, 37(5):824-834Luo Liping, Zeng Yunhui, Luo Zhenguo. Oscillation theorems of quasilinear hyperbolic systems with effect of impulse and delay. Acta Mathematicae Applicatae Sinica, 2014, 37(5):824-834
[6] 罗李平, 罗振国, 曾云辉. 基于脉冲控制的非线性时滞双曲系统的振动分析. 系统科学与数学, 2013, 33(9):1024-1032Luo Liping, Luo Zhenguo, Zeng Yunhui. Oscillation analysis of nonlinear delay hyperbolic systems based on impulsive control. Journal of Systems Science and Mathematical Sciences, 2013, 33(9):1024-1032
[7] Yang J C, Liu A P, Liu G J. Oscillation of solutions to neutral nonlinear impulsive hyperbolic equations with several delays. Electronic Journal of Differential Equations, 2013, 2013(27):1-10
[8] Luo L P, Wang Y Q. Oscillation for nonlinear hyperbolic equations with influence of impulse and delay. International Journal of Nonlinear Science, 2012, 14(1):60-64
[9] Liu A P, Liu T, Zou M. Oscillation of nonlinear impulsive parabolic differential equations of neutral type. Rocky Mountain Journal of Mathematics, 2011, 41(3):833-850
[10] 罗李平, 杨柳. 具高阶Laplace算子的非线性脉冲时滞双曲型方程的振动判据. 系统科学与数学, 2009, 29(12):1672-1678 Luo Liping, Yang Liu. Oscillation criteria for nonlinear impulsive delay hyperbolic equations with higher order Laplace operator. Journal of Systems Science and Mathematical Sciences, 2009, 29(12):1672-1678
[11] Gilbarg D, Trudinger N S. Elliptic Partial Equations of Second Order. Berlin:Springer-Verlag, 1977
[12] Philos Ch G. A new criterion for oscillatory and asymptotic behavior of delay differential equations. Bull Acad Polon Sci Ser Sci Math Astron Phys, 1981, 29(4):367-370

[1]	王丹妮, 杨红丽, 杨联贵. 一类完整Coriolis力作用下的高阶非线性Schrödinger方程[J]. 数学物理学报, 2018, 38(5): 883-892.
[2]	王俊, 王天璐, 温艳华, 周先锋. N维非线性时滞分数阶微分方程初值问题的全局解[J]. 数学物理学报, 2018, 38(5): 903-910.
[3]	谷海波, 高彩霞. 基于Razumikhin-Type理论的中立性随机切换非线性系统的P阶矩稳定性与几乎必然稳定性[J]. 数学物理学报, 2018, 38(5): 970-983.
[4]	王惠文, 曾红娟, 李芳. 多基点分数阶微分方程脉冲边值问题解的存在性[J]. 数学物理学报, 2018, 38(4): 697-715.
[5]	张晓建. 具非线性中立项的广义Emden-Fowler微分方程的振动性[J]. 数学物理学报, 2018, 38(4): 728-739.
[6]	李向东, 傅勤, 吴健荣. 基于有限差分法的二阶双曲型分布参数系统的迭代学习控制[J]. 数学物理学报, 2018, 38(3): 588-598.
[7]	刘灯明, 曾宪忠, 穆春来. 具非线性记忆的高阶阻尼双曲系统的一个爆破结果[J]. 数学物理学报, 2018, 38(2): 304-312.
[8]	叶耀军, 胡月. 一类高阶波动方程的整体解及指数衰减估计[J]. 数学物理学报, 2018, 38(1): 110-121.
[9]	李文娟, 汤获, 俞元洪. 中立型Emden-Fowler微分方程的振动性[J]. 数学物理学报, 2017, 37(6): 1062-1069.
[10]	张宁, 夏铁成. 一个新非线性可积晶格族和它们的可积辛映射[J]. 数学物理学报, 2017, 37(5): 814-824.
[11]	蒋杭进, 尚妍, 吴琼莉. 相依性度量的比较研究[J]. 数学物理学报, 2017, 37(5): 931-949.
[12]	陈传军, 张晓艳, 赵鑫. 一维非线性抛物问题两层网格有限体积元逼近[J]. 数学物理学报, 2017, 37(5): 962-975.
[13]	熊君, 李俊民, 何超. 一阶双曲型偏微分方程的模糊边界控制[J]. 数学物理学报, 2017, 37(3): 469-477.
[14]	王云竹, 高建芳. 一类非线性延迟微分方程θ-方法的数值解振动分析[J]. 数学物理学报, 2017, 37(2): 342-351.
[15]	杨帆, 傅初黎, 李晓晓, 任玉鹏. 一类非线性反向热传导问题的Fourier正则化方法[J]. 数学物理学报, 2017, 37(1): 62-71.