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.