Fixed points of meromorphic solutions of higher order linear differential equations. (English) Zbl 1094.30036

Liu, Mingsheng; Zhang, Xiaomei

Ann. Acad. Sci. Fenn., Math. 31, No. 1, 191-211 (2006).

The authors discuss some interesting problems on the fixed points of meromorphic solutions of higher order linear differential equation \(f^{(k)}+A(z)f=0\) and their derivatives, where \(A(z)\) is a given rational function or a given transcendental meromorphic function of finite order. For every transcendental meromorphic solution \(f\) of \(f^{(k)}+A(z)f=0\), they give its exact order \(\sigma(f)\) and show that the sequence of fixed points of \(f\) and the sequence of fixed points of its derivatives have the same (hyper-)exponent of convergence.

Reviewer: Jianming Chang (Changshu)

MSC:

30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34M05	Entire and meromorphic solutions to ordinary differential equations in the complex domain

Keywords:

linear differential equations; meromorphic solutions; fixed points; (hyper-)order of a meromorphic function; (hyper-)exponent of convergence of a sequence