Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 57, pp. 1-14.

Title: Periodic solutions for neutral functional differential equations
       with impulses on time scales

Authors: Yongkun Li   (Yunnan Univ., China)
         Xiaoyan Dou  (Yunnan Univ., China)
	 Jianwen Zhou (Yunnan Univ., China)

Abstract:
 Let $\mathbb{T}$ be a periodic time scale. We use  Krasnoselskii's
 fixed point theorem to show that the neutral functional differential
 equation with impulses
 $$\displaylines{
  x^{\Delta}(t)=-A(t)x^\sigma(t)+g^\Delta(t,x(t-h(t)))+f(t,x(t),x(t-h(t))),\quad
  t\neq t_j,\;t\in\mathbb{T},\cr
   x(t_j^+)= x(t_j^-)+I_j(x(t_j)), \quad j\in \mathbb{Z}^+
  }$$
  has a periodic solution. Under a slightly more stringent conditions
  we show that the periodic solution is unique using the contraction
  mapping principle.

Submitted August 22, 2011 Published April 10, 2012.
Math Subject Classifications: 34N05, 34K13, 34K40, 34K45.
Key Words: Positive periodic solution; neutral functional differential   
           equations; impulses; Krasnoselskii fixed point; time scales.