Geodesic
On meromorphic solutions of the Riccati differential equations
Ran Ran Zhang1 ; Zong Xuan Chen1
1 School of Mathematical Sciences South China Normal University 510631 Guangzhou, People's Republic of China
Annales Polonici Mathematici, Tome 99 (2010) no. 3, pp. 247-262

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap99-3-3
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

Ran Ran Zhang 1 ; Zong Xuan Chen 1

1 School of Mathematical Sciences South China Normal University 510631 Guangzhou, People's Republic of China 
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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

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