On [p,q]-order of growth of solutions of complex linear differential equations near a singular point

Abstract

We investigate the [p, q]-order of growth of solutions of the following complex linear differential equation f (k) + A k−1 (z) f (k−1) + • • • + A 1 (z) f + A 0 (z) f = 0, where A j (z) are analytic in C − {z 0 }, z 0 ∈ C. Some estimations of [p, q]-order of growth of solutions of the equation are obtained, which is generalization of previous results from Fettouch-Hamouda.

Limit Directions of Julia Sets of Entire Functions and Complex Differential Equations

“…where n(Ω(θ − ε, θ + ε; r), 0,f) denotes the number of zeros of f in Ω(θ − ε, θ + ε; r), counting multiplicities. If λ θ (f) � ρ(f), then the ray arg z � θ is considered to be an accumulation line of the zero sequence of f. Tis concept can be used to analyze the growth of solutions of diferential equations, as described in [18]. Te properties of solutions of the following equation ( 8) are needed in our results.…”