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On the complex oscillation theory of linear differential equations with analytic coefficients in the unit disc. (Chinese. English summary) Zbl 1199.34471
Summary: The complex oscillation theory of linear differential equations of the form $L (f)=f^{ (k)}+A_{k-1} (z)f^{ (k-1)}+\cdots +A_0 (z)f=F (z)\;(k\in {\mathbb N})$ is investigated, where the coefficients $$A_j (z)$$ $$(j=0,\ldots, k-1)$$ and $$F (z)$$ are analytic functions in the unit disc $$\Delta=\{z\,:\,|z|<1\}$$. The authors obtain several precise theorems about the hyper order, the hyper convergence exponent of zero points and fixed points of solutions of differential equations.

##### MSC:
 34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 34M03 Linear ordinary differential equations and systems in the complex domain