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Zbl 1115.34060
Si, Jianguo; Ma, Minghuan
Local invertible analytic solution of a functional differential equation with deviating arguments depending on the state derivative.
(English)
[J] J. Math. Anal. Appl. 327, No. 1, 723-734 (2007). ISSN 0022-247X

The paper deals with the functional differential equation with deviating arguments depending on the state derivative $$x'(z) = 1 / x(az + b x'(z)), \tag 1$$ where $a$ and $b$ are complex numbers. Reducing (1) by change of variables $az + b x'(z) = g(\alpha g^{-1}(z))$ to some auxiliary equation with respect to $g$, the authors prove the existence of local analytic solutions to (1) in the complex field. The complex parameter $\alpha$ is located inside the unit circle $S^1$ or $\alpha \in S^1$ and satisfies some additional non-resonance or resonance conditions.
[Victor I. Tkachenko (Ky{\"\i}v)]
MSC 2000:
*34K05 General theory of functional-differential equations

Keywords: functional differential equation; local analytic solutions

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