Analytic Solutions of an Iterative Functional Differential Equation with State Dependent Delay

摘要

This paper is concerned with a functional differential equation with state dependent delay. By constructing a convergent power series solution of an auxiliary equation, analytic solutions for the original differential equation are obtain. For technical reasons, in previous work the constant α given in the Schroder transformation, is required to fulfill that α is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.