Local Analytic Solutions of a Functional Differential Equation

摘要

Analytic solution are studied for an iterative functional differential equation. For technical reasons, in previous work the constant μ given in the Schroder 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.