**Stability of simple periodic solutions of neutral functional differential equations**

**Z. Shao**, Millersville University, Millersville, U.S.A.**Y. Lu**, Bloomsburg University, Bloomsburg, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 1. (2003), pp. 1-11.

Communicated by G. Makay.
| Appeared on 2003-01-01 |

**Abstract: **We study the stability property of a simple periodic solution of an autonomous neutral functional differential equation (NFDE) of the form

$${d\over dt} D(x_t) = f (x_t).$$

A new proof based on local integral manifold theory and the implicit function theorem is given for the classical result that a simple periodic orbit of the equation above is asymptotically orbitally stable with asymptotic phase. The technique used overcomes the difficulty that the solution operator of a NFDE does not smooth as $t$ increases.

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