JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (03): 57-61.doi: 10.6040/j.issn.1671-9352.0.2014.083

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(Strong) oscillation analysis of quasilinear hyperbolic systems with impulse effect

LUO Li-ping, LUO Zhen-guo, ZENG Yun-hui   

  1. Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang 421002, Hunan, China
  • Received:2014-03-10 Revised:2014-09-30 Online:2015-03-20 Published:2015-03-13

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Abstract: The (strong) oscillation properties of a class of quasilinear hyperbolic systems with impulse effect are investigated. By using a new technique of treating quasilinear diffusion term and some results of impulsive differential inequality, some sufficient criteria are obtained for the (strong) oscillation of all solutions of such systems under second boundary condition. The results fully indicate that the system oscillation are caused by impulse effect.

Key words: (strong) oscillation, impulse effect, quasilinear diffusion term, hyperbolic system

CLC Number: 

  • O175.27
[1] 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[J].系统科学与数学,2013,33(9):1024-1032. LUO Liping, LUO Zhenguo, ZENG Yunhui. Oscillation results of third order half linear neutral differential equations[J]. J Sys Sci & Math Scis, 2013, 33(9):1024-1032.
[2] LUO Liping, LIAO Jiding, GAO Zhenghui. Oscillation of systems of impulsive delay hyperbolic equations[J]. International Journal of Applied Mathematics and Applications, 2008, 1(2):147-154.
[3] 罗李平.具非线性扩散系数的脉冲时滞双曲型方程组的振动性[J].自然科学进展,2008,18(3):341-344. LUO Liping. Oscillation of systems of impulsive delay hyperbolic equations with nonlinear diffusion coefficient[J]. Progress of Natural Science, 2008, 18(3):341-344.
[4] 罗李平,欧阳自根.脉冲中立型时滞抛物偏微分方程组的振动准则[J].应用数学学报,2007,30(5):822-830. LUO Liping, OUYANG Zigen. Oscillation criteria of systems of impulsive neutral delay parabolic partial differential equations[J]. Acta Math Appl Sinica, 2007, 30(5):822-830.
[5] LUO Liping, OUYANG Zigen. Oscillation theorem to systems of impulsive neutral delay parabolic partial differential equations[J]. Ann of Diff Eqs, 2007, 23(3):297-303.
[6] LUO Liping, PENG Baiyu, YANG Liu. Oscillation of systems of impulsive delay parabolic equations about boundary value problems[J]. Ann of Diff Eqs, 2007, 23(4):470-476.
[7] LUO Liping. Oscillation theorem of systems of quasilinear impulsive delay hyperbolic equations[J]. Northeast Math J, 2007, 23(3):255-262.
[8] 罗李平,俞元洪.具拟线性扩散系数的脉冲中立型抛物系统的(强)振动性[J].振动与冲击,2011,30(8):183-186. LUO Liping, YU Yuanhong. (Strong) oscillation for systems of impulsive neutral parabolic equations with quasilinear diffusion coefficient[J]. Journal of Vibration and Shock, 2011, 30(8):193-196.
[9] LI Weinian. On the forced oscillation of solutions for systems of impulsive parabolic differential equations with several delays[J]. J Comput Appl Math, 2005, 181(1):46-57.
[10] LAKSHMIKANTHAM V, BAINOV D D, SIMEONOV P S. Theory of impulsive differential equations[M]. Singapore: World Scientific Publishing Co Pte Ltd, 1989.
[1] LUO Li-ping, LUO Zhen-guo, ZENG Yun-hui. (Full)oscillatory problems of certain quasilinear hyperbolic systems with damping term [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 73-77.
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