Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]