Growth of ({\alpha},\b{eta},{\gamma})-order solutions of linear differential equations with analytic coefficients in the unit disc

TL;DR

This paper investigates the growth behavior of solutions to higher-order complex linear differential equations within the unit disc, focusing on coefficients with finite ({},,)-order, and extends existing theoretical frameworks.

Contribution

It introduces new results on the growth of solutions based on ({},,)-order and type, generalizing prior research in the field.

Findings

Established bounds on solution growth in terms of ({},,)-order

Extended previous results to more general coefficient classes

Provided new theoretical insights into differential equation solutions

Abstract

In this paper, we study the growth of solutions to higher-order complex linear differential equations in the unit disc, where the analytic coefficients are of finite ({\alpha},\b{eta},{\gamma})-order. By employing the concepts of ({\alpha},\b{eta},{\gamma})-order and ({\alpha},\b{eta},{\gamma})-type, we establish new results concerning the growth of such solutions. These results extend and generalize previous work by the second author and by Biswas.