| 关开中，贺小宝.一类具比例时滞的脉冲微分方程解的振动性[J].南华大学学报(自然科学版),2011,25(3):58~62.[GUAN Kai-zhong,HE Xiao-bao.Oscillation of Solutions of a Class of Impulsive DifferentialEquations with Pantograph Delays[J].Journal of University of South China(Science and Technology),2011,25(3):58~62.] |
| 一类具比例时滞的脉冲微分方程解的振动性 |
| Oscillation of Solutions of a Class of Impulsive DifferentialEquations with Pantograph Delays |
| 投稿时间：2011-05-23 |
| DOI： |
| 中文关键词: 脉冲微分方程 比例时滞 正负系数 振动性 |
| 英文关键词:Impulsive differential equation Pantograph delay positive and negative cofficients oscillation |
| 基金项目:湖南省自然科学基金资助项目（11JJ3011） |
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| 中文摘要: |
| 建立一类具比例时滞和正负系数脉冲微分方程解振动的充分条件.所得结果揭示：脉冲微分方程解的振动性可以仅由脉冲条件所引起；在一定脉冲条件下，非脉冲微分方程解的振动性可以被脉冲微分方程所继承.最后举例予以说明. |
| 英文摘要: |
| Sufficient conditions for oscillation of solutions to a class of impulsive differential equations with pantograph delays and positive and negative coefficients are obtained.Our results reveal the fact that the oscillatory properties of all solutions of an impulsive differential equation can only be caused by the impulsive perturbations and that the oscillatory behavior of every solution of the differential equation without impulses can be inherited by the impulsive differential equation under certain impulsive perturbations.Some examples are also given to illustrate the usefulness of our main results. |
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