International Journal of Differential Equations
Volume 2009 (2009), Article ID 145213, 14 pages
Research Article

Analytic Solutions of an Iterative Functional Differential Equation near Resonance

Department of Mathematics, Shandong University of Technology, Zibo, Shandong 255049, China

Received 6 January 2009; Accepted 14 April 2009

Academic Editor: Peiguang Wang

Copyright © 2009 Tongbo Liu and Hong Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown function x′′(z)+cx(z)=x(az+bx(z)) in the complex field . By reducing the equation with the Schröder transformation to the another functional differential equation without iteration of the unknown function λ2g′′(λz)g(z)λg(λz)g′′(z) + c(g(z))2(λg(λz)ag(z)) = (g(z))3(g(λ2z)ag(λz)), we get its local invertible analytic solutions.