The growth, oscillation and fixed points of solutions of complex linear differential equations in the unit disc

摘要

We consider the complex differential equations of the formA_k (z) f~((k)) + A_(k - 1) (z) f~((k - 1)) + ? + A_1 (z) f′ + A_0 (z) f = F (z), where A_0 (≡?0), A_1, ..., A_k and F are analytic functions in the unit disc D = {z ∈ 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.