带强迫项的二阶脉冲时滞微分方程的振动性  

Oscillation of second-order impulsive delay differential equations with forcing term

作　　者：黄木根[1] 冯伟贞[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《黑龙江大学自然科学学报》2006年第4期452-456,共5页Journal of Natural Science of Heilongjiang University

摘　　要：主要讨论一类带强迫项的二阶线性脉冲时滞微分方程x″(t)+p(t)x(t-h)=q(t),≠ttk,k=1,2…,x(tk+)=akx(tk),x′(tk+)=bkx′(tk).解的振动性问题.利用Kartastos技巧,将其转化为不带强迫项的二阶线性脉冲时滞微分方程进行研究,得到若干新的判定此类方程解振动的充分条件.脉冲是一种控制或扰动因素,在这种扰动较大的情况下,用实例说明了本方法也能保证系统解的振动性.Consider the oscillations of second -order linear impulsive delay differential equations with forcing term x＂（t）＋p（t）x（t-h）=q（t）,t≠tk,k=1,2…,x（tk^＋）=akx（tk）,x＇（tk^＋）=bkx＇（tk）. By cill means of Kartsatos technique, reduce it to a second order linear impulsive homogeneous equation. Some new osation criteria in terms of the coefficients are given for the equation part in giving rise to the oscillation of the equations, and it is shown by sure oscillation of solutions. In some cases,impulses play a dominating an example that the obtained result can ensure oscillation of solutions.

关 键 词：振动 二阶 时滞微分方程 脉冲 强迫项 

分 类 号：O175.25[理学—数学]