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Analytic Solutions of an Iterative Functional Differential Equation

✍ Scribed by Xin-Ping Wang; Jian-Guo Si

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 87 KB
Volume: 262
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7527

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✦ Synopsis

This paper is concerned with an iterative functional differential equation x x r z = c 0 z + c 1 x z + c 2 x x z + • • • + c m x m z , where r and m are nonnegative integers, x 0 z = z x 1 z = x z x 3 z = x x x z , etc. are the iterates of the function x z , and m j=0 c j = 0. By constructing a convergent power series solution y z of a companion equation of the form αy α r+1 z = y α r z m j=0 c j y α j z , analytic solutions of the form y αy -1 z for the original differential equation are obtained.

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