Analytic solutions of a class of iterative functional differential equations

摘要

In this paper, we are concerned with the existence of analytic solutions of a class of iterative functional differential equations x′(z) = x(az + bx(z)) + F(z) in the complex field C. Employing the method of majorant series, we need to discuss the constant λ given in Schröder transformation. We discuss not only these λ at a root of the unity, but also those λ near a root of the unity under Brjuno condition.