Abstract
In this paper, the existence of analytic solution of an iterative functional differential equation is studied. By reducing the equation with the Schrooder transformation to the another functional equation with proportional delay, an existence theorem is established for analytic solutions of the original equation. For technical reasons, in previous work the constant β given in the Schroder transformation, is required to satisfy that β is off the unit circle S1 or lies on the circle with the Diophantine condition. In this paper, we give results of analytic solutions in the case of β at resonance, i.e., at a root of the unity and β is near resonance under the Brjuno condition.
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