Abstract: The H-oscillation of a class of second-order vector neutral partial differential equations with damped terms and continuously distributed delays were transformed into the problems of which differential inequalities haven't eventually positive solution by employing the method of reducing dimension with the inner product and making use of Riccati transformation and introducing parameter functions. Some criteria of sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Robin boundary value condition.

Key words: damping, continuously distributed delay, neutral type, partial differential equation, H-oscillation