Abstract and Applied Analysis
Volume 2012 (2012), Article ID 954352, 13 pages
http://dx.doi.org/10.1155/2012/954352
Research Article

Smooth Solutions of a Class of Iterative Functional Differential Equations

Houyu Zhao

School of Mathematics, Chongqing Normal University, Chongqing 401331, China

Received 14 December 2011; Accepted 5 March 2012

Academic Editor: Miroslava Růžičková

Copyright © 2012 Houyu Zhao. 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.

Abstract

By Faà di Bruno’s formula, using the fixed-point theorems of Schauder and Banach, we study the existence and uniqueness of smooth solutions of an iterative functional differential equation 𝑥 ( 𝑡 ) = 1 / ( 𝑐 0 𝑥 [ 0 ] ( 𝑡 ) + 𝑐 1 𝑥 [ 1 ] ( 𝑡 ) + ⋯ + 𝑐 𝑚 𝑥 [ 𝑚 ] ( 𝑡 ) ) .