Existence of periodic solutions for delay differential equations with state dependent delay (Q1265074)

The existence of periodic solutions to a delay differential equation, with delay depending indirectly on the state, of the form \[ \frac {dx}{dt}=-f(x(t-\tau(t))), \quad\text{with}\quad \frac {d\tau}{dt}=h(x(t),\tau(t)) \] is studied. A fixed point problem related to a Poincaré operator is constructed and solved using an ejective fixed point theorem.