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Zbl 1057.34067
Xu, Bing; Zhang, Weinian; Si, Jianguo
Analytic solutions of an iterative functional differential equation which may violate the Diophantine condition.
(English)
[J] J. Difference Equ. Appl. 10, No. 2, 201-211 (2004). ISSN 1023-6198

In the complex domain the following differential equation is considered $$\dot{x}(z)=f\left(\sum_{s=0}^{m}c_s x^s(z)\right),$$ where $f$ is a given function analytic for $\vert z \vert \leq \sigma$ and $\sum_{s=0}^{m}\vert c_s \vert \neq 0$. The existence of an analytic solution is proved.
MSC 2000:
*34K05 General theory of functional-differential equations
34M05 Entire and meromorphic solutions

Keywords: iterative functional differential equation; analytic solution; diophante condition

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