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

Abstract

We consider the complex differential equations of the form A 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.