PERIODIC SOLUTIONS FOR A SECOND-ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATION WITH VARIABLE DELAY

In this work, the hybrid fixed point theorem of Krasnoselskii is used to prove the existence of periodic solutions of the second-order nonlinear neutral differential equation d(2)/dt(2) x(t) + p(t) d/dt x(t) + q(t)x(t) = d/dt g(t, x(t - tau(t))) + f(t, x(t), x(t - tau(t))). We transform the problem into an integral equation and uniqueness of the periodic solution, by means of the contraction mapping principle.