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山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (03): 57-61.doi: 10.6040/j.issn.1671-9352.0.2014.083

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带脉冲效应的拟线性双曲系统(强)振动性分析

罗李平, 罗振国, 曾云辉   

  1. 衡阳师范学院数学与计算科学系, 湖南 衡阳 421002
  • 收稿日期:2014-03-10 修回日期:2014-09-30 出版日期:2015-03-20 发布日期:2015-03-13
  • 作者简介:罗李平(1964- ), 男, 教授, 研究方向为(脉冲)偏微分系统解的性态.E-mail:luolp3456034@163.com
  • 基金资助:
    湖南省"十二五"重点建设学科资助项目(湘教发[2011]76号);湖南省自然科学基金青年资助项目(13JJ4098)

(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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摘要： 研究了一类带脉冲效应的拟线性双曲系统(强)振动性质。利用新的处理拟线性扩散项的技巧及脉冲微分不等式的某些结果, 获得了该类系统在第二类边界条件下所有解(强)振动的若干充分判据, 结论充分地表明系统振动是由脉冲效应引起的。

关键词: 双曲系统, 拟线性扩散项, 脉冲效应, (强)振动性

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

中图分类号: 

  • 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] 罗李平,罗振国,曾云辉. 一类带阻尼项的拟线性双曲系统的(全)振动性问题[J]. 山东大学学报（理学版）, 2016, 51(6): 73-77.
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