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 ) ) where r > 0 , F , G ∈ C ( R 1 ) . It is shown that if F is nondecreasing on R 1 , and some additional assumptions hold, then the ω limit set of every bounded solution of such a equation with some initial conditions is composed of r -periodic solutions. Our results are new and complement some corresponding ones already known.