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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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