We investigate the growth and Borel exceptional
values of meromorphic solutions of the Riccati differential equation
$$
w'=a(z)+b(z)w+w^2,
$$
where $a(z)$ and $b(z)$ are meromorphic functions. In particular, we
correct a result of E. Hille [Ordinary Differential Equations
in the Complex Domain, 1976] and get a precise estimate on the
growth order of the transcendental meromorphic solution $w(z)$; and
if at least one of $a(z)$ and $b(z)$ is non-constant, then we show
that $w(z)$ has at most one Borel exceptional value. Furthermore, we
construct numerous examples to illustrate our results.
Keywords:
investigate growth borel exceptional values meromorphic solutions riccati differential equation w where meromorphic functions particular correct result hille ordinary differential equations complex domain get precise estimate growth order transcendental meromorphic solution least non constant has borel exceptional value furthermore construct numerous examples illustrate results
Affiliations des auteurs :
Ran Ran Zhang
1
;
Zong Xuan Chen
1
1
School of Mathematical Sciences South China Normal University 510631 Guangzhou, People's Republic of China
@article{10_4064_ap99_3_3,
author = {Ran Ran Zhang and Zong Xuan Chen},
title = {On meromorphic solutions of the {Riccati} differential equations},
journal = {Annales Polonici Mathematici},
pages = {247--262},
year = {2010},
volume = {99},
number = {3},
doi = {10.4064/ap99-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap99-3-3/}
}
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AU - Ran Ran Zhang
AU - Zong Xuan Chen
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Ran Ran Zhang; Zong Xuan Chen. On meromorphic solutions of the Riccati differential equations. Annales Polonici Mathematici, Tome 99 (2010) no. 3, pp. 247-262. doi: 10.4064/ap99-3-3
