Oscillations of a delay differential equation with piecewise constant arguments (Q1919030)

The authors consider the differential-difference equation \[ x'(t)+px(t-1)+qx([t-1])=0,\tag{1} \] where \(p,q\in(0,\infty)\) and \([\cdot ]\) denotes the greatest integer function. Main result of the paper: A necessary and sufficient condition for the oscillation of (1) is that its characteristic equation \((pz+q)\exp(pz^{-1})-(p+q)=0\) has no roots in \((0,1)\).