Bifurcation of periodic solutions in a nonlinear difference-differential equations of neutral type

The existence of a self-sustained periodic solution in the autonomous equation \[ u’\left ( \tau \right ) - \alpha u’\left ( {\tau - h} \right ) + \beta u\left ( \tau \right ) + \alpha \gamma u\left ( {\tau - h} \right ) = \epsilon f\left ( {u\left ( \tau \right )} \right )\] is proved under appropriate assumptions on $\alpha ,\beta ,\gamma ,f$ and $h$. The method of proof consists in converting this equation into an equivalent nonlinear integral equation and demonstrating the convergence of an appropriate iteration scheme.