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Smooth solutions of a nonhomogeneous iterative functional differential equation

Published online by Cambridge University Press:  14 November 2011

Jian-Guo Si  and
Sui Sun Cheng
Jian-Guo Si
Affiliation:
Department of Mathematics, Binzhou Normal College, Binzhou, Shandong, 256604, P.R. China
Sui Sun Cheng
Affiliation:
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C.
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Abstract

This paper is concerned with an iterative functional differential equation x(t) = c1x(t) + c2x[2](t) + … cmχ[m](t) + F(t), where x[i](t) is the i-th iterate of the function x(t). By means of Schauder's Fixed Point Theorem, we establish a local existence theorem for smooth solutions which also depend continuously on the forcing function F(t).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 821 - 831
Copyright
Copyright © Royal Society of Edinburgh 1998

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