Local analytic solutions of a functional differential equation

Abstract

Analytic solution are studied for an iterative functional differential equation. For technical reasons, in previous work the constant μ given in the Schröder transformation, is required to satisfy that μ is off the unit circle S 1 or lies on the circle with the Diophantine condition. In this paper, we study results of analytic solutions in the case of μ at a root of the unity and the case of μ near resonance under the Brjuno condition. Analytic solutions of neutral differential-difference equation are also discussed. © 2012 Springer-Verlag.