Basic and Recent Results in Neutral Differential Equations
by
Youssef Raffoul
University of Dayton

The authors Zhixiang Li, Xiao Wang of the paper

[1] Existence of positive periodic solutions for neutral functional differential equations, Electron. J. Diff. Eqns., Vol. 2006(2006), No. 34, pp. 1-8

attempted to prove the existence of positive periodic solutions of the nonlinear neutral differential equation

d dt [x(t) - ax(t-t)] = r(t)x(t)- f(t, x(t-t))

by using cone theory. It was pointed out that the results in the paper are not correct since the two sets W₁ and W₂ that were constructed by the authors are not open in the Banach space. For the same reason, an addendum has been added to the paper.
The main aim of this research is to give a correct proof for the existence of a positive periodic solution by using a different fixed point theorem from the one used in [1].

Date received: September 17, 2007