脉冲扰动对非线性时滞双曲型分布参数系统振动的影响

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

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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

CLC Number:

O175.27

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.

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[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

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