Growth of Solutions of Certain Linear Differential Equations With Dominant Coefficient of Lower [p, q]−Order Near a Singular Point

Abstract

In this article, we study the growth of solutions to certain linear differential equations with analytic coefficients in C − {z₀}, where z₀ ∈ C is an essential singularity. We derive estimates for the lower bounds of the [p, q]-order of these solutions. Our results improve and extend the previous findings of Liu, Long and Zeng, and those of Long and Zeng.