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The growth, oscillation and fixed points of solutions of complex linear differential equations in the unit disc. (English) Zbl 1160.34357
Summary: We consider the complex differential equations of the form $$A_k(z)f^{(k)}+_{Ak - 1}(z)f^{(k - 1)}+\dots +A_1(z)f'+A_0(z)f=F(z)$$, where $$A_0 (\not\equiv 0)$$, $$A_1,\dots ,A_k$$ and $$F$$ are analytic functions in the unit disc $$D=\{z\in\mathbb{C}:|z|<1\}$$. Some results on the finite iterated order and the finite iterated convergence exponent of zero points in $$D$$ of meromorphic (analytic) solutions are obtained. The fixed points of solutions of differential equations are also investigated in this paper.

##### 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
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