A periodic solution of a differential equation with state-dependent delay

We study a differential equation for delayed negative feedback which models a situation where the delay depends on the present state and becomes effective in the future. The main result is existence of a periodic solution in case the equilibrium is linearly unstable. The proof employs the ejective fixed point principle on a compact convex set K0⊂C([−h,0],R) of Lipschitz continuous functions and uses that the equation generates a smooth semiflow on an infinite-dimensional submanifold of the space C1([−h,0],R).