Growth of $(\alpha ,\beta ,\gamma )$-order solutions of linear differential equations with entire coefficients

TL;DR

This paper investigates the growth behavior of solutions to higher order linear differential equations with entire coefficients, using generalized growth measures called $(eta ,eta ,eta)$-order and type, extending previous results.

Contribution

It introduces generalized growth concepts for solutions of differential equations, improving and broadening earlier findings by Kinnunen, Long, and Bela"{i}.

Findings

Derived new bounds for solution growth rates.

Generalized growth measures encompass previous results.

Extended the classification of solution behaviors.

Abstract

The main aim of this paper is to study the growth of solutions of higher order linear differential equations using the concepts of $(\alpha ,\beta ,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-type. We obtain some results which improve and generalize some previous results of Kinnunen \cite{13}, Long et al. \cite{L} as well as Bela\"{\i}di \cite{b3}, \cite{b5}.