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

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
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