Analytic solutions for iterative functional differential equations

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.

Keywords

• Iterative differential equation
• existence
• analytic solution
• polynomial solution