Dynamic behavior for a class of neutral functional differential equations

Consider the neutral functional differential equation (x(t)−x(t−r))′=−F(x(t))+G(x(t−r))(x(t)−x(t−r))′=−F(x(t))+G(x(t−r)) where r>0r>0, FF, G∈C(R1)G∈C(R1). It is shown that if FF is nondecreasing on R1R1, and some additional assumptions hold, then the ωω limit set of every bounded solution of such a equation with some initial conditions is composed of rr-periodic solutions. Our results are new and complement some corresponding ones already known.