Existence of positive periodic solutions for a neutral Lienard equation with a singularity of repulsive type

The periodic problem is studied in this paper for the neutral Lienard equation with a singularity of repulsive type (x(t) - cx (t - sigma))'' + f(x(t))x'(t) + phi(t)x(t - tau) - r(t)/x mu(t) = h(t), where f : [0, +infinity -> R is continuous, r : R -> (0, +infinity) and phi : R -> Rare continuous with T-periodicity in the t variable, c,mu,sigma,tau are constants with vertical bar c vertical bar > 1, mu > 1, 0 < sigma, tau < T.Many authors obtained the existence of periodic solutions under the condition |c| > 1.The proof of the main result relies on a continuation theorem of coincidence degree theory established by Mawhin.