一类非线性脉冲中立抛物型分布参数系统的振动条件

Abstract

Abstract:

The oscillation problems for a class of nonlinear impulse parabolic distributed parameter systems with neutral term and higher order Laplace operator are investigated under first boundary value condition. By using the technique of treating neutral term and higher order Laplace operator and integral averaging method, some new sufficient criteria are established for the oscillation of all solutions of such systems. The conclusions fully indicate that the system oscillation is caused by impulse and delay.

Key words: Oscillation, Parabolic distributed parameter system, Impulse, Nonlinear neutral term, Higher order Laplace operator

CLC Number:

O175.26

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.

Trendmd

References 12

1	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. 数学物理学报, 2018, 38A (2): 313- 321
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- 472
3	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- 30
4	Ma Q X , Liu A P . Oscillation criteria of neutral type impulsive hyperbolic equations. Acta Mathematica Scientia, 2014, 34B (6): 1845- 1853
5	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
6	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- 834
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	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- 1032
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
11	Gilbarg D , Trudinger N S . Elliptic Partial Equations of Second Order. Berlin: Springer-Verlag, 1977
12	Lakshmikantham V, Bainov D D, Simeonov P S. Theory of Impulsive Differential Equations. Singapore: World Scientific Publishing Co Pte Ltd, 1989

[1]	Wangjin Yao. Existence and Multiplicity of Solutions for a Coupled System of Impulsive Differential Equations via Variational Method [J]. Acta mathematica scientia,Series A, 2020, 40(3): 705-716.
[2]	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.
[3]	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.
[4]	Jimeng Li. Oscillation Analysis of Second-Order Generalized Emden-Fowler-Type Delay Differential Equations [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1041-1054.
[5]	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.
[6]	Wenjuan Li,Shuhai Li,Yuanhong Yu. Oscillation of Second Order Nonlinear Neutral Differential Equations with Distributed Delay [J]. Acta mathematica scientia,Series A, 2019, 39(4): 812-822.
[7]	Bo Zhu,Lishan Liu. Existence and Uniqueness of the Mild Solutions for a Class of Fractional Non-Autonomous Evolution Equations with Impulses [J]. Acta mathematica scientia,Series A, 2019, 39(1): 105-113.
[8]	Wang Huiwen, Zeng Hongjuan, Li Fang. An Existence Result for Impulsive Boundary Value Problem for Fractional Differential Equations with Multiple Base Points [J]. Acta mathematica scientia,Series A, 2018, 38(4): 697-715.
[9]	Wang Huiling, Gao Jianfang. Oscillation Analysis of Analytical Solutions for a Kind of Nonlinear Neutral Delay Differential Equations with Several Delays [J]. Acta mathematica scientia,Series A, 2018, 38(4): 740-749.
[10]	Zhang Xiaojian. Oscillation of Generalized Emden-Fowler Differential Equations with Nonlinear Neutral Term [J]. Acta mathematica scientia,Series A, 2018, 38(4): 728-739.
[11]	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.
[12]	Yang Jiashan, Li Tongxing. Oscillation for a Class of Second-Order Damped Emden-Fowler Dynamic Equations on Time Scales [J]. Acta mathematica scientia,Series A, 2018, 38(1): 134-155.
[13]	Li Wenjuan, Tang Huo, Yu Yuanhong. Oscillation of the Neutral Emden-Fowler Differential Equation [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1062-1069.
[14]	Wang Yunzhu, Gao Jianfang. Oscillation Analysis of Numerical Solutions in the θ-Methods for a Kind of Nonlinear Delay Differential Equation [J]. Acta mathematica scientia,Series A, 2017, 37(2): 342-351.
[15]	Zeng Yunhui, Luo Liping, Yu Yuanhong. Oscillation Criteria for Generalized Neutral Emden-Fowler Equations [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1067-1081.

Oscillation Conditions of Certain Nonlinear Impulsive Neutral Parabolic Distributed Parameter Systems

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 12

Related Articles 15

Metrics

Comments

Recommended 10