Abstract:

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.

Key words:  impulse; vector; delay; hyperbolic partial functional differential equation; H-oscillation