On meromorphic solutions of the Riccati differential equations

• Autorzy: Ran Ran Zhang , Zong Xuan Chen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 34M05: Entire and meromorphic solutions
• 30D35: Distribution of values, Nevanlinna theory
• 34A34: Nonlinear equations and systems, general

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2010
• Tom: 99
• Numer: 3
• Strony: 247-262

Daty

wydano

2010

Twórcy

autor

Ran Ran Zhang

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

autor

Zong Xuan Chen

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

Identyfikatory

DOI

10.4064/ap99-3-3