具脉冲和时滞效应的拟线性双曲系统的振动性定理  

Oscillation Theorems of Quasilinear Hyperbolic Systems with Effect of Impulse and Delay

作　　者：罗李平[1] 曾云辉[1] 罗振国[1] 

机构地区：[1]衡阳师范学院数学与计算科学系,衡阳421002

出　　处：《应用数学学报》2014年第5期824-834,共11页Acta Mathematicae Applicatae Sinica

基　　金：湖南省"十二五"重点建设学科项目(湘教发[2011]76号);湖南省自然科学基金青年项目(13JJ4098)资助

摘　　要：本文讨论一类具脉冲和时滞效应的拟线性双曲系统的强振动性和振动性,利用Green公式和Neumann边值条件将该类系统的振动问题转化为二阶脉冲时滞微分不等式最终正解的不存在性问题,并利用脉冲微分不等式,得到了该类系统强振动和振动的若干充分性判据.所得结果充分表明系统振动是由脉冲和时滞效应引起的.The strong oscillation and oscillation for a class of quasilinear hyperbolic sys- tems with the effect of impulse and delay are discussed. By using Green＇s formula and Neumann boundary condition, the oscillatory problems to the systems are reduced to the nonexistence problems of eventually positive solutions of two order impulsive delay differ- ential inequality, and thereby some sufficient criteria are obtained for the strong oscillation and oscillation of such systems via impulsive differential inequality. The obtained results fully indicate that the system oscillation is caused by the effect of impulse and delay.

关 键 词：脉冲 时滞双曲系统 强振动性 振动性 拟线性 

分 类 号：O175.27[理学—数学]