An existence theorem for a retarded functional differential equation (Q1900404)

The author studies the periodic boundary value problem associated to the equation (1) \(x'(t) = g(x(t)) (f(x(t)) - h(t,x (t - \tau))) + p(t)\), where \(g,f,h,p : R \to R\) are continuous functions, \(\tau > 0\) is a real number, \(p\) and \(h\) are \(T\) periodic functions. Under general assumptions there is proved that (1) has at least one \(T\)-periodic solution, which is independent on \(\tau\).