On meromorphic solutions of the Riccati differential equations

Ran Ran Zhang, and Zong Xuan Chen. "On meromorphic solutions of the Riccati differential equations." Annales Polonici Mathematici 99.3 (2010): 247-262. <http://eudml.org/doc/280793>.

@article{RanRanZhang2010,
abstract = { We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², 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. },
author = {Ran Ran Zhang, Zong Xuan Chen},
journal = {Annales Polonici Mathematici},
keywords = {Riccati differential equations; growth order; meromorphic solution; Borel exceptional value},
language = {eng},
number = {3},
pages = {247-262},
title = {On meromorphic solutions of the Riccati differential equations},
url = {http://eudml.org/doc/280793},
volume = {99},
year = {2010},
}

TY - JOUR
AU - Ran Ran Zhang
AU - Zong Xuan Chen
TI - On meromorphic solutions of the Riccati differential equations
JO - Annales Polonici Mathematici
PY - 2010
VL - 99
IS - 3
SP - 247
EP - 262
AB - We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², 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.
LA - eng
KW - Riccati differential equations; growth order; meromorphic solution; Borel exceptional value
UR - http://eudml.org/doc/280793
ER -