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Analytic solutions of an iterative differential equation under Brjuno condition

Authors:

Affiliation:

1.School of Science,University of Ji’nan,Ji’nan,P.R. China;2.School of Mathematics,Shandong University,Ji’nan,P.R. China

Abstract:

In this paper, the differential equation involving iterates of the unknown function,

$ x'(z) = [a^2 - x^2 (z)]x^{[m]} (z) $ x'(z) = [a^2 - x^2 (z)]x^{[m]} (z)

Keywords:	iterative differential equation analytic solution Banach fixed point theorem resonance Diophantine condition Brjuno condition
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