Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 180, pp. 1-7.

Title: Analytic solutions for iterative functional differential equations
 
Author: Pingping Zhang (Sichuan Univ., Chengdu, China)

Abstract:
 Because of its technical difficulties the existence of analytic
 solutions to the iterative differential equation
 $x'(z)=x(az+bx(z)+c x'(z))$ is a source of open problems.
 In this article we obtain analytic solutions, using Schauder's fixed
 point theorem. Also we present a unique solution which is a nonconstant
 polynomial in the complex field.

Submitted June 7, 2012. Published October 16, 2012.
Math Subject Classifications: 34K05, 39B12, 39B32.
Key Words: Iterative differential equation; existence; 
           analytic solution; polynomial solution.