Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 102, pp. 1-7.
Title: Periodic solutions for neutral nonlinear differential
equations with functional delay
Author: Youssef N. Raffoul (Univ. of Dayton, Dayton, OH, USA)
Abstract:
We use Krasnoselskii's fixed point theorem to show that
the nonlinear neutral differential equation with functional delay
$$
x'(t) = -a(t)x(t)+ c(t)x'(t-g(t))+ q\big(t, x(t), x(t-g(t)\big)
$$
has a periodic solution. Also, by transforming the problem to an
integral equation we are able, using the contraction mapping
principle, to show that the periodic solution is unique.
Submitted April 22, 2003. Published October 6, 2003.
Math Subject Classifications: 34K20, 45J05, 45D05.
Key Words: Krasnoselskii; neutral; nonlinear; integral equation;
periodic solution; unique solution.