Periodic solutions for a neutral nonlinear dynamical equation on a time scale

Let T be a periodic time scale. We use a fixed point theorem due to Krasnosel’ski˘ı to show that the nonlinear neutral dynamic system with delay x (t)=−a(t)xσ (t) +c(t)x (t −k) +q t,x(t),x(t − k) , t∈ T, has a periodic solution. We assume that k is a fixed constant if T = R and is a multiple of the period of T if T = R. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle.  2006 Elsevier Inc. All rights reserved