Periodic boundary value problems for the second order functional differential equations (Q1888234)

The authors consider the periodic boundary value problem \[ -y''(t)=f(t,y(t),y(\theta(t))), \qquad t\in[0,T], \quad y(0)=y(T),\qquad y'(0)=y'(T), \] where \(f:[0,T]\times \mathbb R^2\to \mathbb R\) is continuous, and \(0\leq \theta(t)\leq t\) for \(t\in[0,T]\). Conditions guaranteeing the existence of extremal solutions to the problem considered are established via the monotone iterative technique.