Generic oscillations of delay differential system with impulses. (Q1416420)

The authors consider the linear functional system \[ X^{\prime}(t)+AX(t)+BX(t-\tau )=0,\quad t\geq t_{0},\;t\neq t_{k},\tag{*} \] with the linear impulsive condition \[ X(t_{k}^{+})-X(t_{k})=C_{k}X(t_{k}),\quad k=1,2,\dots \tag{**} \] They compare the oscillation and nonoscillation of the impulsive systems (*) and (**) with nonimpulsive systems which recently have been used by some authors especially in the oscillation of nonlinear delay impulsive differential equations. By using properties of the characteristic equation, they establish some explicit sufficient conditions for generic oscillations and for generic nonoscillations. The definitions of the generic oscillation and generic nonoscillation are also included.