Periodic boundary value problems for a class of functional differential equations (Q1919580)

The authors employ the method of upper and lower solutions and monotone iterative technique to establish, under some assumptions, existence of a solution of the periodic boundary value problem for functional differential equations of the form \(u'(t) = f(t,u(t), u(h(t)))\), \(t \in [0,T]\), \(u(0) = u(T)\), where \(f \in C ([0,T] \times \mathbb{R}^2, \mathbb{R})\), \(h \in C([0,T], [- r,T])\), \(r > 0\), \(t - r \leq h(t) \leq t\) for \(t \in [0,T]\). An example is given to illustrate the results.