Necessary and Sufficient Conditions for Oscillation of Autonomous Neutral Differential Equations with Distributed Delay

In the paper the autonomous neutral differential equation with distributed delay [formula] is considered,where δi= ±1, i=1,2. It is proved that if r1(τ−1) ≠ r1(τ+1), then the necessary and sufficient condition for all solutions of this equation to oscillate is that its corresponding characteristic equation [formula] have no real roots.