脉冲向量时滞双曲型偏微分方程的振动判据

考虑一类脉冲向量时滞双曲型偏微分方程的振动性,利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲时滞微分不等式不存在最终正解的问题,获得了该类方程在Dirichlet边值条件下所有解H-振动的充分判据。此外,利用二阶脉冲时滞微分不等式,还获得了该类方程所有有界解H-振动的一个充分判据,这里H是Rm中的单位向量。

Oscillation criteria of impulsive vector delay hyperbolic partial differential equations

The oscillations of a class of impulsive vector delay hyperbolic partial differential equations are considered. To change the multi-dimensional oscillation problems into the problems of which one-dimensional impulsive delay differential inequalities have not an eventually positive solution by employing the concept of H-oscillation introduced by Domslak and the method of reducing dimension with the inner product, some sufficient criteria for H-oscillation of all solutions of the equations are obtained under Dirichlet’s boundary value condition. Also, by using the second order impulsive delay differential inequalities, a sufficient criterion for H-oscillation of all bounded solutions of the equations is presented, where H is a unit vector of Rm.