Infinite order solutions of second order linear differential equations

TL;DR

This paper investigates second order linear differential equations with entire coefficients and establishes conditions under which all non-trivial solutions exhibit infinite order growth.

Contribution

It provides new results linking coefficient conditions to the infinite order growth of solutions, advancing understanding of differential equations with entire coefficients.

Findings

Solutions have infinite order under certain coefficient conditions

Conditions on coefficients determine the growth rate of solutions

The results extend previous knowledge on differential equations with entire coefficients

Abstract

This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.