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Analytic solutions of an iterative functional differential equation which may violate the Diophantine condition. (English) Zbl 1057.34067

In the complex domain the following differential equation is considered

$\stackrel{˙}{x}\left(z\right)=f\left(\sum _{s=0}^{m}{c}_{s}{x}^{s}\left(z\right)\right),$

where $f$ is a given function analytic for $|z|\le \sigma$ and ${\sum }_{s=0}^{m}|{c}_{s}|\ne 0$. The existence of an analytic solution is proved.

MSC:
 34K05 General theory of functional-differential equations 34M05 Entire and meromorphic solutions (ODE)