Oscillation of impulsive neutral delay differential equations

Abstract

In this paper, effective sufficient conditions for the oscillation of all solutions of impulsive neutral delay differential equations of the form [x(t) - P(t)x(t - τ)]′ + Q(t)x(t - σ)λsgn x(t - σ) = 0, t ≥t0, x(tk+) = bkx(tk), k - 1,2,... are established. Our results reveal the fact that the oscillatory properties of all solutions of Eqs. (*) and (**) may be caused by the impulsive perturbations (**) though the corresponding neutral delay differential equation without impulses, i.e., Eq. (*), admits a nonoscillatory solution. It is also seen that the oscillatory behavior of all solutions of Eq. (*) can be inherited by Eqs. (*) and (**) under certain impulsive perturbations (**). Some examples are also given to illustrate the applicability of the results obtained. © 2002 Elsevier Science (USA).