Analytic Solutions of an Iterative Functional Differential Equation
This paper is concerned with the existence of analytic solutions of an iterative functional differential equation. By constructing a convergent power series solution of an auxiliary equation, analytic solutions for the original differential equation are obtained. We discuss not only those α at the hyperbolic case 0<|α|<1 but also those α near resonance under Diophantine condition.
L. X. Liu "Analytic Solutions of an Iterative Functional Differential Equation", Key Engineering Materials, Vols. 474-476, pp. 2208-2212, 2011