Periodic solutions of the neutral Duffing Equations

We consider the following neutral delay Dung equation ax 00 (t) + bx 0 (t) + cx(t) + g(x(t 1); x 0 (t 2); x 00 (t 3)) = p(t) = p(t + 2 ); where a, b and c are constants, i, i = 1; 2; 3, are nonnegative constants, g : R R R ! R is continuous, and p(t) is a continuous 2 -periodic function. In this paper, combining the Brouwer degree theory with a continuation theorem based on Mawhin's coincidence degree, we obtain a sucien t condition for the existence of 2 -periodic solution of above equation.