Electron. J. Diff. Equ., Vol. 2012 (2012), No. 180, pp. 1-7.

Analytic solutions for iterative functional differential equations

Pingping Zhang

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.

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Pingping Zhang
Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: zhangpingpingmath@163.com

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