Analytic Solutions of a Nonhomogeneous Iterative Functional Differential Equation
This paper is concerned with an iterative functional differential equation with state-dependent delay As well as in previous works, we reduce this problem with the Schroeder transformation to obtain auxiliary equation. For technical reasons, in previous work the constantgiven in the Schroeder transformation, is required to fulfill that is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we discuss not only thoseat a root of the unity, but also those near resonance under the Brjuno condition.
L. X. Liu "Analytic Solutions of a Nonhomogeneous Iterative Functional Differential Equation", Key Engineering Materials, Vols. 474-476, pp. 2155-2160, 2011