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.
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {98},
year = {2010},
pages = {247-262},
zbl = {1214.34086},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-3-3}
}
Ran Ran Zhang; Zong Xuan Chen. On meromorphic solutions of the Riccati differential equations. Annales Polonici Mathematici, Tome 98 (2010) pp. 247-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-3-3/